Problem 7-28 A student selects his answers on a true/false examination by tossing a coin (so that any particular answer has a .50 probability of being correct). He must answer at least 70% correctly in order to pass. Find his probability of passing when the number of questions is

Answers

Answer 1

To find the probability of passing the true/false examination when the number of questions is n, we need to use binomial distribution. We need to plug in the values and calculate the probability of passing for a specific number of questions n

Let X be the number of correct answers the student gets. Since the probability of getting a correct answer is 0.50, we have X ~ Bin(n, 0.50).

To pass the exam, the student must answer at least 70% of the questions correctly. This means that X must be greater than or equal to 0.70n. We can write this as:

P(X >= 0.70n) = 1 - P(X < 0.70n)

Using the binomial distribution formula, we can find the probability of getting less than 0.70n correct answers:

P(X < 0.70n) = ∑(i=0 to 0.70n-1) (n choose i) * 0.50^i * 0.50^(n-i)

We can use a calculator or software to evaluate this sum. For example, if n = 50, we get:

P(X < 0.70n) = P(X < 35) = 0.0738

Therefore, the probability of passing the exam when the number of questions is 50 is:

P(X >= 0.70n) = 1 - P(X < 0.70n) = 1 - 0.0738 = 0.9262

So, the student has a 92.62% chance of passing the exam if there are 50 true/false questions and he answers them by tossing a coin.


To find the probability of passing the true/false examination with a 70% correct answer requirement, we will use the binomial probability formula. The binomial probability formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
- P(X = k) is the probability of getting k correct answers out of n questions
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of getting a correct answer (0.50 in this case)
- n is the number of questions
- k is the number of correct answers

Since we need to find the probability of passing when the number of questions is not specified, let's assume there are n questions. To pass the exam, the student must answer at least 70% of the questions correctly. Therefore, k must be greater than or equal to 0.7n.

The probability of passing the exam can be calculated by summing up the probabilities of getting at least 70% correct answers:

P(passing) = sum(P(X = k)) for k = ceil(0.7n) to n

Where ceil() is the ceiling function that rounds up to the nearest integer.

Now we need to plug in the values and calculate the probability of passing for a specific number of questions n. Please provide the number of questions on the examination to get the exact probability of passing.

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Related Questions

On a toll road, there are 7 lanes for drivers to pay their toll. Customer arrival times are random, with an exponential distribution. Service times are random, with an exponential distribution. What is the proper description for this queueing system.

Answers

Queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.

The queueing system you have described can be modeled as an M/M/7 queue, where:

M represents that inter-arrival times and service times are exponentially distributed.

M represents that the arrival process is memoryless, meaning that the probability of a customer arriving at any given time does not depend on the previous arrival times or the state of the system.

7 represents the number of service channels, or lanes, available for customers to pay their toll.

The notation for this system is M/M/7, which indicates that it has an infinite queue capacity and that there is no limit to the number of customers that can be waiting in the queue.

In this queueing system, customers arrive randomly and independently, and they join the queue if all lanes are busy. They are served on a first-come, first-served basis, with the service times also being exponentially distributed.

This queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.

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A. Graph A
B. Graph B
C. Graph C
D. Graph D

Answers

The graph of the inequality is graph B.

What is an inequality graph?

The graph of inequality can be a dashed line or a solid line which shows the part of the number line that contains the values on the graph that will satisfy the inequality.

Given that:

y - 5 > 2x - 10

Let's first move all the terms that do not have y to the other side of the equation. So,

y > 2x - 10 + 5

y > 2x - 5

Using the slope intercept form y = mx + b, where:

m = slope  b = y-intercept

Thus,

slope = 2, and y-intercept = -5.

Since the inequality sign is greater than(>), then the straight line will be a dashed straight line, and we will then shade the area above the boundary line.

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Consider a sampling distribution formed based on n = 3. The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements σ.

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The standard deviation of the population of all sample means is approximately 0.577 times less than the standard deviation of the population of individual measurements σ.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

The standard deviation of the sampling distribution of sample means is smaller than the standard deviation of the population of individual measurements (σ) by a factor of 1/√n, where n is the sample size.

This is known as the standard error of the mean (SE) and is calculated as SE = σ/√n.

So, in this case, where n = 3, the standard deviation of the sampling distribution of sample means will be σ/√3, which is approximately 0.577 times σ.

Therefore, the standard deviation of the population of all sample means is approximately 0.577 times less than the standard deviation of the population of individual measurements σ.

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A quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is the value of the quantity after 47 years, to the nearest hundredth

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The value of the quantity after 47 years is approximately 4071.38.

To find the value of the quantity after 47 years, we'll use the formula for continuous compound growth:

Final Value = Initial Value * (1 + Growth Rate) ^ Time

Here, Initial Value = 3600, Growth Rate = 2.5% (which is 0.025 as a decimal), and Time = 47 years.

However, the growth rate is given per decade. So, first, we need to convert the time into decades:

Time (in decades) = 47 years / 10 years/decade = 4.7 decades

Now, we can use the formula:

Final Value = 3600 * (1 + 0.025) ^ 4.7

Final Value ≈ 3600 * (1.025) ^ 4.7
Final Value ≈ 3600 * 1.130939

Now, rounding the final value to the nearest hundredth:

Final Value ≈ 4071.38

So, the value of the quantity after 47 years is approximately 4071.38.

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Answer Immeditely Please

Answers

The length of segment AD is given as follows:

AD = 4.

What is the geometric mean theorem?

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

Hence, in this problem, we have that the altitude of BD = 2 is the geometric mean of DC = 1 and AD, hence:

AD x 1 = 2²

AD = 4 units.

Which is the length of segment AD.

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We want to test if the proportion of BYU students who identify as Democrat and support the death penalty is less than the proportion of BYU students who identify as Republican and support the death penalty. What is our alternative hypothesis

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The alternative hypothesis would be: The proportion of BYU students who identify as Democrat and support the death penalty is significantly less than the proportion of BYU students who identify as Republican and support the death penalty.

The alternative hypothesis for this test would be: The proportion of BYU students who identify as Democrat and support the death penalty (p1) is less than the proportion of BYU students who identify as Republican and support the death penalty (p2). Mathematically, it can be written as:

H1: p1 < p2

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A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98, with a standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk

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The 98% confidence interval to estimate the true cost of a gallon of milk is  between $2.9334 and $3.0266.

How to find the  98% confidence interval to estimate the true cost of a gallon of milk

The following formula can be used to compute a confidence interval for a population mean with a known population standard deviation:

CI = xbar ± z*(σ/√n)

Here, X = $2.98, = $0.10, n = 25, and a 98% confidence interval is desired.

The z-score at a 98% confidence level is 2.33

When we plug in the values, we get:

CI = 2.98 ± 2.33*(0.10/√25) = 2.98 ± 0.0466 = [2.9334, 3.0266]

As a result, we can be 98% certain that the genuine cost of a gallon of milk is between $2.9334 and $3.0266.

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Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus is jan correct?

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Answer:

Jan is not correct.

Every rhombus is a parallelogram, but not every parallelogram is a rhombus.

a car radiator contains 5 liters of a 25% solution of antifreeze. how many liters must be removed and then replaced bya 75% antifreeze solution to leave the radiator filled with a 55% sltuion

Answers

To leave the radiator filled with a 55% antifreeze solution, 3 liters of the 25% solution of antifreeze must be removed and replaced with 3 liters of a 75% antifreeze solution.

We start by calculating the amount of antifreeze in the initial solution. Since the solution is 25% antifreeze, the amount of antifreeze in the solution is 25% of 5 liters, or 1.25 liters.

Let x be the amount of 75% antifreeze solution that must be added. We can set up the equation for the amount of antifreeze in the final solution as follows:

1.25 - 0.25(3) + 0.75x = 0.55(5)

Simplifying and solving for x, we get:

x = 3

Therefore, 3 liters of the 25% antifreeze solution must be removed from the radiator and replaced with 3 liters of the 75% antifreeze solution to leave the radiator filled with a 55% antifreeze solution.

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What is the probability that in a randomly selected composition of n has a second part and it is equal to 1

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The probability of selecting a composition of n with a second part equal to 1 is equal to (n-1)/4.

Let us consider a composition of n as an ordered sequence of positive integers where the sum of the integers is n.

The number of compositions of n is equal to 2ⁿ⁻¹,

Since there are n-1 spaces between the numbers where we can choose to either include or exclude a separator.

To calculate the probability that a randomly selected composition of n has a second part equal to 1,

Consider the second part of the composition.

It can be any positive integer from 1 to n-1, inclusive.

For the second part to be equal to 1,

Choose 1 as the second number in the composition and distribute the remaining n-2 among the remaining slots.

There are n-1 slots left since the second slot is already occupied by the number 1.

The remaining n-2 can be distributed in 2ⁿ⁻³ ways, since there are n-3 spaces left to distribute the remaining numbers.

Therefore, the probability of selecting a composition of n with a second part equal to 1 is,

P = (n-1) ×  2ⁿ⁻³ / 2ⁿ⁻¹

  = ( n - 1 ) × 2ⁿ⁻³⁻ⁿ⁺¹

   =  ( n - 1 ) × 2⁻²

  = (n-1) / 4

Therefore, the probability is equal to  (n-1)/4.

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a.They need to elect a slate of officers including a president, vice president, recording secretary, corresponding secretary, treasurer, historian, and statistician. If each of the members can be elected to any of the positions and each member may only hold one position, how many different slates of officers can be elected

Answers

Therefore, The number of different slates of officers that can be elected is 5,040. This is calculated using the permutation formula with 7 positions to fill and 7 members who can be elected to each position.


To find the number of different slates of officers that can be elected, we need to use the permutation formula. The formula for permutations is n!/(n-r)!, where n is the total number of items and r is the number of items selected. In this case, we have 7 positions to fill and 7 members who can be elected to each position. Therefore, the number of different slates of officers that can be elected is 7!/(7-7)! = 7! = 5,040.
There are seven positions that need to be filled including president, vice president, recording secretary, corresponding secretary, treasurer, historian, and statistician. Each member can be elected to any position and can only hold one position. To find the number of different slates of officers that can be elected, we use the permutation formula. We have 7 positions to fill and 7 members who can be elected to each position, so the number of different slates of officers that can be elected is 7!/(7-7)! = 7! = 5,040.

Therefore, The number of different slates of officers that can be elected is 5,040. This is calculated using the permutation formula with 7 positions to fill and 7 members who can be elected to each position.

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Recent studies show that approximately 65% of people are lactose intolerant (have trouble digesting milk products). If a group of 10 people are randomly selected, what is the probability that exactly 8 of those selected are lactose intolerant

Answers

The probability of exactly 8 people in a group of 10 being lactose intolerant is 0.4182, or about 41.82%.

To calculate the probability of selecting exactly 8 lactose intolerant people from a group of 10, we can use the binomial distribution formula:

[tex]P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)[/tex]

where P(X = k) is the probability of selecting k lactose intolerant people, n is the total number of people in the group (10 in this case), p is the probability of selecting a lactose intolerant person (0.65), and C(n, k) is the number of ways of selecting k lactose intolerant people from n people.

Using the formula, we get:

[tex]P(X = 8) = C(10, 8) \times 0.65^8 \times (1 - 0.65)^{(10 - 8)[/tex]

= 45 × 0.17850625 × 0.4225

= 0.4182

Therefore, the probability of exactly 8 people in a group of 10 being lactose intolerant is 0.4182, or about 41.82%.

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10. Given f(x) = 41, find (F-1)(1). = 4.2 9 (a) 1 1 (b) (c) ) 1 4 i (d) 4 (e) 2

Answers

To find (F-1)(1) for the given function f(x) = 41, we need to find the inverse function F-1(x), which is simply 41. Then, we evaluate F-1(1) to get the answer of 4.

The given function f(x) = 41 is a constant function, meaning that it has the same output value of 41 for every input value of x. In order to find (F-1)(1), we need to find the inverse function of f(x), denoted as F-1(x), and then evaluate F-1(1).

To find the inverse function, we need to switch the roles of x and f(x) in the function f(x) = 41 and solve for x. This gives us x = 41, which means that the inverse function is F-1(x) = 41. This is because F-1(f(x)) = x, so F-1(41) = x.

Now, we can evaluate F-1(1) by substituting 1 for x in the inverse function. This gives us F-1(1) = 41. Therefore, the answer is (d) 4.

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Suppose that I have a sample of 25 women and they spend an average of $100 a week dining out, with a standard deviation of $20. The standard error of the mean for this sample is $4. Create a 95% confidence interval for the mean and wrap words around your results.

Answers

We can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26.

Based on the given information, we can calculate a 95% confidence interval for the mean amount that women in the population spend dining out per week. With a sample size of 25 and a standard error of $4, we can use the formula:

95% CI = sample mean +/- (critical value x standard error)

To find the critical value, we need to look up the t-distribution with degrees of freedom (df) = n-1 = 24 and a significance level of alpha = 0.05/2 = 0.025 (since we are interested in a two-tailed test). From a t-table or calculator, we find that the critical t-value is approximately 2.064.

Plugging in the values, we get:

95% CI = $100 +/- (2.064 x $4)
95% CI = $100 +/- $8.26
95% CI = ($91.74, $108.26)

Therefore, we can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26. This means that if we were to repeatedly take random samples of 25 women and calculate their mean amount spent dining out, about 95% of the intervals we construct using this method would contain the true population mean.

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Suppose you calculated a paired-samples t test, with 30 pairs of scores. Mean mean difference is 6 and the standard error is 2.1. What is the .95 confidence interval

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This means that we can be 95% confident that the true population means difference lies between 1.7075 and 10.2925.

Confidence interval = Mean difference ± (t-value × standard error)

Substituting the given values into the formula, we get:

Confidence interval = 6 ± (2.045 × 2.1)

Confidence interval = 6 ± 4.2925

A confidence interval is a statistical concept used to estimate the range of values in which a population parameter is likely to fall. It is calculated using sample data and is used to provide an estimate of the true population parameter.

The confidence interval is a range of values that is constructed around a point estimate, such as the sample mean or proportion. This range is based on the level of confidence chosen by the researcher, typically 90%, 95%, or 99%. For example, a 95% confidence interval means that if we were to repeat the sampling process many times, we would expect the true population parameter to fall within the range of values calculated for 95% of those samples.

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A three-dimensional figure is formed by a rectangular prism and an
isosceles triangular prism as shown in the diagram below.
10 ft
27 ft
29 ft
17 ft
15ft
Use the information given in the image to find the surface area of the
composite figure.
A

Answers

The surface area of the composite figure is calculated to be 3719 square feets.

How to calculate for the total surface area of the composite figure

area of one identical triangle = 1/2 × 27ft × 10ft = 135ft²

area of two identical triangle = 270ft²

area of one top identical rectangle face = 27ft × 17ft = 493ft²

area of one top identical rectangle face = 986ft²

area of one bigger identical side rectangle = 29ft × 15ft = 435ft²

area of two bigger identical side rectangle = 870ft²

area of one smaller identical side rectangle = 27ft × 15ft = 405ft²

area of two smaller identical side rectangle = 810ft²

area of bottom rectangle = 28ft × 27ft = 783ft²

surface area of the figure = 270ft² + 986ft² + 870ft² + 810ft² + 783ft²

surface area of the figure = 3719ft².

Therefore, the surface area of the composite figure is calculated to be 3719 square feets.

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The critical value in a chi-square test for independence depends on Multiple Choice the normality of the data. the variance of the data. the number of categories. the expected frequencies.

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The critical value in a chi-square test for independence depends on the number of categories and expected frequencies, and not on the normality or variance of the data.

The critical value in a chi-square test for independence is determined by the number of categories and expected frequencies in the data. This test is used to analyze the relationship between two categorical variables, and the expected frequencies are calculated based on the assumption of independence between these variables. The critical value is the minimum value of the test statistic that would result in rejecting the null hypothesis, which states that the two variables are independent.

The normality and variance of the data do not affect the critical value in a chi-square test for independence. This test does not assume a normal distribution of the data, and the variance is not used to calculate the expected frequencies. Instead, the expected frequencies are determined by the marginal frequencies of the two variables, assuming that they are independent.

It is important to use the correct critical value in a chi-square test for independence, as using the wrong value could result in incorrect conclusions about the relationship between the two variables. The critical value can be found using a chi-square distribution table or calculator, based on the number of categories and the level of significance chosen for the test.

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The FDA regulates that fresh Albacore tuna fish contains at most 0.82 ppm of mercury. A scientist at the FDA believes the mean amount of mercury in tuna fish for a new company exceeds the ppm of mercury. A test statistic was found to be 2.576 and a critical value was found to be 1.645, what is the correct decision and summary

Answers

the test statistic is 2.576 and the critical value is 1.645.

Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the mean amount of mercury in tuna fish for the new company exceeds 0.82 ppm.

To make a decision in this scenario, we need to use a hypothesis test. Let's set up the null and alternative hypotheses:

Null hypothesis (H0):

The mean amount of mercury in the tuna fish produced by the new company is less than or equal to 0.82 ppm.

Alternative hypothesis (Ha):

The mean amount of mercury in the tuna fish produced by the new company is greater than 0.82 ppm.

The test statistic is 2.576 and the critical value is 1.645.

Since the test statistic is greater than the critical value and is in the rejection region of the null hypothesis, we reject the null hypothesis.

we cannot say for certain whether this difference is statistically significant without knowing the sample size, the standard deviation of the sample, and the level of significance.

Reject the null hypothesis at the chosen significance level (which we don't have in this case), which suggests that the mean amount of mercury in the tuna fish produced by the new company is likely to be greater than 0.82 ppm.

This means that we have evidence to suggest that the mean amount of mercury in the tuna fish produced by the new company exceeds 0.82 ppm, as suspected by the scientist at the FDA.

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I dont understand what im supposed to do after i do the 2pir2 + 2pirh which i got 50.24. but what do i do abouth the whole radius = diameter/2 ?

Answers

The surface area of the cylinder, given the diameter, can be found to be 18. 84 inch .

How to find the surface area ?

The surface area of a cylinder can be found by the formula :

= 2 π r ² + 2 π h

The radius can be found to be:

= Diameter / 2

= 2 / 2

= 1 inch

The value of π is 3. 14.

This means the surface area would be:

= (2 x 3. 14 x 1 x 1) + (2 x 3. 14 x 1 x 2 )

= 6. 28 + 12. 56

= 18. 84 inch

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To verify that all sales that have been shipped to customers have been recorded, a test of transactions should be completed on a representative sample drawn from:

Answers

To verify that all sales that have been shipped to customers have been recorded, a test of transactions should be completed on a representative sample drawn from the sales records or shipping records.

The sample should be chosen randomly and be large enough to provide a reasonable level of confidence in the accuracy of the recorded transactions. This test will help ensure that all sales have been properly recorded in the accounting system and that there are no unrecorded sales. It is important to perform this test on a regular basis to maintain the integrity of the financial records.

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Suppose we write down the smallest (positive) $2$-digit, $3$-digit, and $4$-digit multiples of $8$. What is the sum of these three numbers

Answers

The sum of the smallest positive 2-digit, 3-digit, and 4-digit multiples of 8 is 11,120.

How to find the smallest positive multiples of 8 that are two-digit, three-digit, and four-digit numbers, and then find the sum of these three numbers?

To be a multiple of 8, a number must be divisible by 8, which means its last three digits must form a multiple of 8. Also, the first digit of the number cannot be 0, since it must be a two-digit number or larger.

Let's start with the two-digit multiple of 8. The smallest two-digit multiple of 8 is 16, which is not a three-digit or four-digit number. The next multiple of 8 is 24, which is also not a three-digit or four-digit number. The smallest two-digit multiple of 8 that is also a three-digit number is 104 (since 112 is not a multiple of 8).

Similarly, the smallest two-digit multiple of 8 that is also a four-digit number is 1008 (since 992 is not a multiple of 8).

Therefore, the three numbers we are looking for are 104, 1008, and 1008, with a sum of:

104 + 1008 + 10008 = 11120

So the sum of the smallest positive 2-digit, 3-digit, and 4-digit multiples of 8 is 11,120.

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Suppose your TA is applying to graduate schools. His chances to be admitted to each school are 5% and are the same for any school. How many different schools does he need to apply to if he wants his chance to be admitted to at least one school to be above 90%, 95%

Answers

We get x = 59. Therefore, your TA should apply to 59 schools to have a greater than 95% chance of being admitted to at least one school.

To calculate the number of different schools your TA needs to apply to in order to have a certain chance of being admitted to at least one school, we can use the formula:

n = log(1 - p) / log(1 - q)

Where n is the number of schools, p is the desired probability of being admitted to at least one school (i.e. 0.9 or 0.95), and q is the probability of not being admitted to any one school (i.e. 0.95).

Using this formula with p = 0.9 and q = 0.95, we get:

n = log(1 - 0.9) / log(1 - 0.05)
n ≈ 14

So your TA would need to apply to at least 14 different schools to have a chance of being admitted to at least one school above 90%.

Using the same formula with p = 0.95 and q = 0.95, we get:

n = log(1 - 0.95) / log(1 - 0.05)
n ≈ 29

So your TA would need to apply to at least 29 different schools to have a chance of being admitted to at least one school above 95%.
To determine the number of schools your TA needs to apply to in order to have at least a 90% and 95% chance of being admitted to at least one school, we'll use the concept of complementary probability.

Step 1: Calculate the probability of NOT being admitted to any school
The probability of not being admitted to a single school is 95% (100% - 5%).

Step 2: Use complementary probability to find the required probability
Let x be the number of schools your TA needs to apply to. The probability of not being admitted to any of the x schools is (0.95)^x.

Step 3: Find the number of schools for a 90% chance
We want the probability of being admitted to at least one school to be above 90%. Therefore, we want the complementary probability to be less than 10% (100% - 90%):
(0.95)^x < 0.10

Solving for x, we get x = 45. Therefore, your TA should apply to 45 schools to have a greater than 90% chance of being admitted to at least one school.

Step 4: Find the number of schools for a 95% chance
Similarly, for a 95% chance, we want the complementary probability to be less than 5% (100% - 95%):
(0.95)^x < 0.05

Solving for x, we get x = 59. Therefore, your TA should apply to 59 schools to have a greater than 95% chance of being admitted to at least one school.

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How many definite integrals would be required to represent the area of the region enclosed by the curves and , assuming you could not use the absolute value function?

Answers

The curves y = x and y = 1 - x^2 intersect at the points (-1, 0), (0, 0), and (1, 0). The region enclosed by these curves is a triangle with vertices at these points.

To find the area of this region without using the absolute value function, we can split the triangle into two parts: the part above the x-axis and the part below the x-axis.

For the part above the x-axis, the bounds of integration are x = 0 to x = 1. The integrand is y = x, the equation of the upper curve. The integral is:

∫[0,1] x dx = 1/2

For the part below the x-axis, the bounds of integration are x = -1 to x = 0. The integrand is y = 1 - x^2, the equation of the lower curve. However, since we cannot use the absolute value function, we need to split this integral into two parts as well. When x is between -1 and 0, the lower curve is y = 1 - x^2, and when x is between 0 and 1, the lower curve is y = x. Therefore, we have:

∫[-1,0] (1 - x^2) dx + ∫[0,1] x dx

Evaluating the first integral gives:

∫[-1,0] (1 - x^2) dx = x - (x^3/3) evaluated from -1 to 0 = 1/3

Therefore, the area of the region enclosed by the curves is:

1/2 + 1/3 = 5/6

So, the area of the region can be represented using two definite integrals.

The volume of a rectangular box is 343 ft3. If the width is 4 times longer than the height, and the length is 16 times longer than the height, find the dimensions of the box.

Answers

The dimensions of the rectangular box are height = 7 ft, width = 28 ft, and length = 112 ft.

Let the height of the box be h. Then, the width is 4h, and the length is 16h. We know that the volume of the box is 343 ft³, so we can set up the equation: V = l*w*h = (16h)(4h)(h) = 64h³

64h³ = 343

h³ = 343/64 = 27/4

h = (27/4)^(1/3) = 3/2

So the height of the box is 3/2 ft. Using this value, we can find the width and length:

Width = 4h = 4(3/2) = 6 ft

Length = 16h = 16(3/2) = 24 ft

Therefore, the dimensions of the rectangular box are height = 7 ft, width = 28 ft, and length = 112 ft.

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6. Median income is $35,000 per year for a truck driver, $3,400 per
month for a middle school teacher, and $450 per week for a bank
teller.

b. Compare the incomes of a truck driver and a bank teller over 20
years.

Answers

Over 20 years, the truck driver would earn more than the bank teller, with a total income of $700,166.40 compared to $468,000 for the bank teller.

We have,

To compare the incomes of a truck driver and a bank teller over 20 years, we need to first convert their incomes to a comparable time period.

Assuming that they work for the same number of weeks in a year, we can use the following conversions:

Truck driver:

$35,000 per year = $673.08 per week

Bank teller:

$450 per week = $23,400 per year

Now, if we assume that their incomes remain constant over the 20-year period, we can calculate their total incomes as follows:

Truck driver:

= $673.08 per week x 52 weeks per year x 20 years

= $700,166.40

Bank teller:

= $450 per week x 52 weeks per year x 20 years

= $468,000

Therefore,

Over 20 years, the truck driver would earn more than the bank teller, with a total income of $700,166.40 compared to $468,000 for the bank teller.

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IF triangle ABC is isosceles, angle B is the vertex angle, AB = 20x - 2, BC = 12x + 30, and AC = 25x, find x and the length of each side of the triangle.

Answers

Answer:

x=-2.5(ERROR)

Step-by-step explanation:

An isosceles triangle is a triangle with two sides of equal length, called legs. The third side of the triangle is called the base. The vertex angle is the angle between the legs 1.

Since triangle ABC is an isosceles triangle with vertex angle B, we know that AB = AC.

Therefore, we can set up an equation:

20x - 2 = 25x

Solving for x:

20x - 25x = 2

-5x = 2

x = -2/5

Since x cannot be negative, there must be an error in the problem statement.

I hope this helps!

What might you lead you to expect that a Poisson distribution might be a good model for the number of hits on each sector? Fit a Poisson distribution to the data by taking λ to be the average number of hits per sector. Use this λ to compute the theoretical frequencies of 0, 1, 2, 3, 4 and 5 hits in 576 sectors. What can you say about the targeting process?

Answers

The Poisson distribution provides a useful tool for analyzing the frequency of hits on each sector and understanding the targeting process.

The Poisson distribution is a good model for situations where events occur randomly and independently over time or space, and the events are rare. In this case, the number of hits on each sector could be considered a rare event, as it is unlikely for a sector to be hit multiple times in a short period of time. Therefore, we might expect a Poisson distribution to be a good model for the number of hits on each sector. To fit a Poisson distribution to the data, we can calculate the average number of hits per sector, which is the parameter λ for the Poisson distribution. Then, we can use this λ to compute the theoretical frequencies of 0, 1, 2, 3, 4, and 5 hits in 576 sectors. Based on the results of the Poisson distribution, we can say that the targeting process is somewhat random, as the actual frequencies of hits on each sector closely match the theoretical frequencies predicted by the Poisson distribution. However, there may be some factors that influence the targeting process, as the actual frequencies of hits do not match the theoretical frequencies perfectly.

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Consider a circular function that tracks the height, h, of a point traversing a unit circle centered at (0,0), h=f(d) where d is the distance traveled around the circle from the starting point (1, 0). What is the exact value of f(pi)?

Answers

The exact value of f(pi) is 0 since when the point on the unit circle has traveled pi distance from its starting point (1,0), it will be at the same height as the starting point.

Let us consider a point on a unit circle centered at (0,0), starting at the point (1,0) and moving around the circle for a distance d. As the point moves around the circle, its height, h, above the x-axis will vary. To find the exact value of f(pi), we need to determine the height of the point when it has traveled a distance of pi around the circle.

When the point has traveled half the distance around the circle, i.e., pi/2, it will be at the point (-1,0), and its height will be 0 since it is on the x-axis. As the point continues to move around the circle, its height will increase until it reaches its maximum height at the point (0,1), where its height is 1.

As the point continues to move around the circle, its height will decrease until it reaches point (1,0), where its height is again 0. Therefore, f(pi) is equal to the height of the point when it has traveled a distance of pi around the circle, which is equal to the height of the point when it is at the point (1,0). Thus, f(pi) = 0.

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what is
15+28+12+20=

Answers

Answer: 75

Step-by-step explanation:

To find the sum of these numbers, we simply add them together:

15 + 28 + 12 + 20 = 75

Therefore, the sum of 15, 28, 12, and 20 is 75.

An important application of the chi-square distribution is a. testing for goodness of fit b. testing for the independence of two variables c. both of the above d. none of the above

Answers

An important application of the chi-square distribution is testing for goodness of fit and testing for the independence of two variables The correct answer is c. both of the above.

The chi-square distribution is a probability distribution that is used in statistics for hypothesis testing and confidence interval estimation. Two important applications of the chi-square distribution are testing for goodness of fit and testing for the independence of two variables.

Testing for goodness of fit involves comparing observed data to expected data, and determining whether the differences between the observed and expected data are statistically significant. The chi-square distribution is used to calculate a test statistic, which measures the degree of divergence between the observed and expected data.

Testing for the independence of two variables involves examining whether there is a relationship between two categorical variables. The chi-square distribution is used to calculate a test statistic that measures the degree of dependence or independence between the two variables. If the test statistic is large enough, it indicates that there is a significant relationship between the two variables.

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