Diameter measurements of 200 roller bearings made by a lathe for one week showed a mean of 1.824 inches and a sample standard deviation of 0.064 inches. What is the 95% confidence interval of the mean diameter of all roller bearings

The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.

Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:

f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70

To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:

P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4

Similarly, we can rewrite the numerator as:

P(X > 60 and X > 55) = P(X > 60)

since if X is greater than 60, it is also greater than 55.

Now, to find P(X > 60), we integrate the density function from 60 to 70:

P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2

Putting it all together:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

= P(X > 60) / P(X > 55)

= (1/2) / (1/4)

= 2

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When employees have different responsibilities, those relationships can be modeled with multiple associations between the employee class and the linked class.

In object-oriented programming, a class is a blueprint for creating objects that have similar properties and behaviors. One of the key concepts in class design is associations, which represent relationships between classes. Associations are used to define how objects of one class are connected to objects of another class.

When employees have different responsibilities, it means that there are multiple ways in which they can be associated with other classes. For example, a software company may have a class of employees who are responsible for developing software, and another class of employees who are responsible for testing the software. Each of these classes has a different set of responsibilities and requires different skills and knowledge.

To model these relationships, we can create multiple associations between the employee class and the linked class. For example, we could create one association between the employee class and the software development class, and another association between the employee class and the software testing class. Each of these associations would have different attributes, such as the employee's role, responsibilities, and qualifications.

By modeling these relationships with multiple associations, we can create more accurate and flexible class designs that reflect the real-world relationships between employees and their responsibilities. This approach also allows us to easily modify or extend the class design as the requirements change, without having to make major changes to the existing code. Overall, multiple associations provide a powerful tool for designing robust and adaptable class structures.

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The height of the carpenter's creation is 8 feet and the width is 7 feet.

To solve this problem, we can use two equations. The first equation is based on the relationship between the width and height:

width = 3(height) - 17

The second equation is based on the amount of lumber the carpenter has available:

2(width) + 2(height) = 30

We can substitute the first equation into the second equation to solve for height:

2(3(height) - 17) + 2(height) = 30

6(height) - 34 + 2(height) = 30

8(height) = 64

height = 8

Using the first equation, we can solve for the width:

width = 3(8) - 17 = 24 - 17 = 7

Therefore, the height is 8 feet and the width is 7 feet.

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Answer:

P = $140 (the principal amount)

r = 6% per year (the annual interest rate)

n = 12 (the number of times the interest is compounded per year, since it is compounded monthly)

t = 15 years (the time period)

A(15) = $140(1 + 0.06/12)^(12*15)

A(15) = $140(1 + 0.005)^180

A(15) = $281.49

It appears that your question is related to the validity of a test measuring academic ability in high school students and its correlation with freshman year college grades. The terms are "predictive validity" and "correlation."

When a test of academic ability given to high school students is found to be correlated with grades during the freshman year at college, it indicates that the test has predictive validity. Predictive validity refers to the extent to which a test or assessment can effectively predict an individual's future performance or outcome. In this case, the academic ability test serves as a predictor of the students' academic performance in their first year of college.

A positive correlation between the test scores and college grades means that higher test scores are generally associated with better college grades and vice versa. This relationship suggests that the test is a useful tool for predicting academic success at the college level. However, it is important to keep in mind that correlation does not necessarily imply causation, and there may be other factors influencing the students' performance in college.

In conclusion, a test of academic ability given to high school students that is correlated with freshman year college grades demonstrates predictive validity, suggesting that the test can effectively predict future academic success. The correlation between the test scores and college grades is an essential consideration when evaluating the usefulness of such a test in predicting academic performance at the college level.

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The conditions at the bottom of the Mariana Trench are vastly different from those in a typical bathtub. The water pressure at that depth is extreme, with over 8 tons of pressure per square inch. In contrast, the water pressure in a bathtub is negligible. Additionally, the water in the Mariana Trench is near freezing, while the water in a bathtub is typically warm or hot. Overall, the conditions in the Mariana Trench are incredibly harsh and inhospitable, making it one of the most extreme environments on Earth.
The Mariana Trench is the deepest part of the ocean at 39,069 feet. The conditions there differ significantly from those in your bathtub. In the Mariana Trench, the water pressure is incredibly high, reaching over 1,000 atmospheres. The temperature is near freezing, ranging from 34-39°F (1-4°C). In contrast, the conditions in your bathtub usually involve much shallower water, lower pressure, and warmer temperatures for a comfortable bathing experience.

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The absolute maximum value of f on the interval [-1,3] is -3 and the absolute minimum value is approximately -1.732.

To find the absolute maximum and minimum values of f(t) = t - (3/t) on the interval [-1, 3], we need to perform the following steps:

1. Find the critical points by taking the derivative of the function and setting it to zero.
2. Evaluate the function at the critical points and the endpoints of the interval.
3. Compare the values to determine the absolute maximum and minimum.

Step 1: Find the critical points.

f(t) = t - (3/t)
To find the derivative, use the power rule and the quotient rule:
f'(t) = 1 - (-3/t^2) = 1 + 3/t^2

Set the derivative equal to zero and solve for t:
1 + 3/t^2 = 0
3/t^2 = -1
t^2 = 3/-1
Since there are no real solutions for t^2 = -3, there are no critical points.

Step 2: Evaluate the function at the endpoints of the interval.

f(-1) = -1 - (3/-1) = -1 + 3 = 2
f(3) = 3 - (3/3) = 3 - 1 = 2

Step 3: Compare the values.
Evaluating f at the critical point and at the endpoints of the interval, we get:
f(-1) = -4
f(3) = -3
f(√3) = √3 - 3/√3 ≈ -1.732
Since there are no critical points and the values at the endpoints are equal, the absolute maximum and minimum values are both 2. Therefore, the absolute maximum and minimum values of the function on the interval [-1, 3] are both 2.

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The mean is 172, the variance is 34.4, and the standard deviation is 5.86.

The United States has a system of bicameralism, which means that each state has two chambers in its legislature: a lower chamber (such as the Assembly or House of Representatives) and an upper chamber (such as the Senate).

The number of constituents per district in each chamber varies from state to state, and it is usually determined by the state's constitution or by a state redistricting commission.

As of the 2010 census, Texas had about 811,147 constituents per state senate district.

However, this is not the highest number of constituents per senator among all the states.

In fact, the state with the highest number of constituents per senator is California.

According to the U.S. Census Bureau, as of the 2010 census, California had a population of approximately 37.3 million people.

The state's constitution provides for 40 state senators, which means that each senator represents approximately 933,000 constituents.

This is significantly higher than the number of constituents per senator in Texas.

The high number of constituents per senator in California can be attributed to the state's large population and the fact that the number of state senators has not kept up with population growth.

The last time the number of state senators in California was increased was in 1973, when the state's population was around 20 million people.

In conclusion, while Texas has a high number of constituents per state senate district, it is not the only state with a high number of constituents per senator.

California has a significantly higher number of constituents per senator, due to its large population and the fact that the number of state senators has not kept up with population growth.

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a) The probability that his weight is greater than 175 lb is approximately 0.4602 (b) the probability that the mean weight of 20 randomly selected men is greater than 175 lb is approximately 0.6772.

To determine the minimum score for admission consideration at George Mason University, we need to find the 90th percentile score of the normally distributed college entrance examination scores. The mean score is 550 and the standard deviation is 100.

Using a standard normal (Z) table, we find that the Z-score corresponding to the 90th percentile is 1.28. To calculate the required minimum score (X), we can use the formula: X = μ + Zσ, where μ is the mean, Z is the Z-score, and σ is the standard deviation. Thus, X = 550 + (1.28)(100) = 550 + 128 = 678. An applicant must score at least 678 to be considered for admission.

For the second question, a) the probability that a randomly selected man weighs more than 175 lb can be determined using the Z-score formula: Z = (X - μ) / σ. Plugging in the values, Z = (175 - 172) / 29 ≈ 0.10. Checking the Z-table, we find the probability to be approximately 0.4602.

b) To find the probability that the mean weight of 20 randomly selected men is greater than 175 lb, we first determine the standard error (SE) of the sample mean using the formula: SE = σ / √n, where σ is the population standard deviation and n is the sample size. In this case, SE = 29 / √20 ≈ 6.48. Now, we calculate the Z-score: Z = (175 - 172) / 6.48 ≈ 0.46. Referring to the Z-table, the probability is approximately 0.6772.

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The corresponding matrix is equal to its transpose conjugate, satisfying the property of Hermitian operators.

To demonstrate that a Hermitian operator Q has matrix elements satisfying Qmn = Qnm*, we first need to understand the properties of Hermitian operators and orthonormal bases.

A Hermitian operator Q is defined as an operator that satisfies Q† = Q, where Q† is the adjoint of Q. In the context of matrix representations, this means that the Hermitian matrix is equal to its conjugate transpose.

An orthonormal basis consists of a set of orthogonal unit vectors, which means that any two distinct vectors in the set have a dot product equal to zero, and the dot product of a vector with itself equals one.

Now, let's consider the matrix elements Qmn and Qnm. Given an orthonormal basis {|n⟩} and a Hermitian operator Q, we can write:

Qmn = ⟨m|Q|n⟩
Qnm = ⟨n|Q|m⟩

To prove the relationship Qmn = Qnm*, we need to show that the adjoint of the operator Q acts on the basis states in the following manner:

⟨m|Q†|n⟩ = ⟨n|Q|m⟩*

Since Q is Hermitian, we have Q† = Q, which gives us:

⟨m|Q|n⟩ = ⟨n|Q|m⟩*

This equation shows that the matrix element Qmn is equal to the complex conjugate of the matrix element Qnm.

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To use the trapezoidal rule to estimate the definite integral of the function f(x) = 1/2x^3+10 on the interval [1,3], we need to divide the interval into n subintervals of equal width h, where h = (b-a)/n = (3-1)/4 = 1/2.

Then, we can use the following formula to approximate the definite integral:

∫1^3 (1/2x^3+10) dx ≈ h/2 * [f(a) + 2∑f(xi) + f(b)]

where xi = a + ih for i = 1, 2, ..., n-1.

Applying this formula with n = 4, we get:

∫1^3 (1/2x^3+10) dx ≈ 1/4 * [f(1) + 2f(5/2) + 2f(2) + 2f(7/2) + f(3)]

where f(x) = 1/2x^3+10.

Evaluating f at the endpoints and midpoints of the subintervals, we obtain:

f(1) = 1/2(1)^3+10 = 10.5

f(5/2) = 1/2(5/2)^3+10 = 27.125

f(2) = 1/2(2)^3+10 = 11

f(7/2) = 1/2(7/2)^3+10 = 35.875

f(3) = 1/2(3)^3+10 = 19.5

Plugging these values into the formula, we get:

∫1^3 (1/2x^3+10) dx ≈ 1/4 * [10.5 + 2(27.125) + 2(11) + 2(35.875) + 19.5]

≈ 27.25

To calculate the absolute error, we need to find the exact value of the definite integral:

∫1^3 (1/2x^3+10) dx = [1/8x^4+10x]1^3 = 99/8

The absolute error is then given by:

|∫1^3 (1/2x^3+10) dx - 27.25| = |99/8 - 27.25| = 219/8

Therefore, the exact value of the absolute error is 219/8.

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The amount of cream in the coffee cup and the amount of coffee in the pitcher of cream remain the same.

When a spoonful of cream is taken from the pitcher and put into the coffee cup, the amount of cream in the pitcher decreases and the amount of cream in the coffee cup increases.

However, when a spoonful of the mixture is put back into the pitcher, the amount of cream in the pitcher increases again and the amount of cream in the coffee cup decreases.

Since the amount of coffee in the pitcher and the cup remains constant throughout this process, there is no net increase or decrease in the amount of coffee or cream in either container.

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This hypothesis aims to determine if the random sample of 2,000 U.S. adults taking an average of 5,863 steps per day with a standard deviation of 2,870 is strong evidence to support the claim that U.S. adults take fewer steps than the 7,000 steps threshold.

The alternative hypothesis in this scenario would be that the average number of steps taken by U.S. adults is less than 7,000 per day. This hypothesis is being tested to determine if there is strong evidence that the true average number of steps per day is lower than the commonly accepted average. The random sample of 2000 U.S. adults helps to ensure that the results are representative of the larger population. The alternative hypothesis for this study would be: "On average, U.S. adults take fewer than 7,000 steps per day."

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The length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

First, we find the angle opposite the side length 5 as follows;

180 - (34 + 118) = 28 {sum of interior angles of a triangle}

Using the sine rule;

5/sin28° = ?/sin34°

? = (5 × sin34°)/sin28° {cross multiplication}

? = 5.9556

Therefore, the length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.

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Answer:

Step-by-step explanation:

Given, 12 / (-4) * 3 + 5

Here we can use the BODMAS rule and solve this problem.

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Now, let’s solve this by applying the BODMAS rule.

In the given sum we can find the Brackets in (-4).

12 / -4 * 3 + 5

There is no Of in this sum.

Let’s gust ignore it.

12 / -4 * 3 + 5

In this sum we can Divide 12 and -4.

-3 * 3 + 5

In this sum we can Multiply -3 and 3.

-9 + 5

In this sum we can Add -9 and 5.

-4

Using the central angle theorem, the degree measure of x is 53°.

The length of AB is 18.8 units.

Given a circle.

We have the central angle theorem,

We have that the angle subtended by an arc of a circle at the center is twice the angle subtended by the same arc at any point on the circle.

Here, the arc is semicircle.

Angle subtended by semicircle at the center= 180°

So, ∠ADB = 180° / 2 = 90°

Interior angles of a triangle sum up to 180°.

x = 180 - (37 + 90) = 53°

sin (x) = BD / AB

sin (53) = 15 / AB

AB = 15 / sin (53)

AB = 18.78 ≈ 18.8 units

Hence the measure of x is 53° and the length of AB is 18.8 units.

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The null hypothesis is that the mean shearing strength of the rivets is equal to or greater than 725 lbs. The alternative hypothesis is that the mean shearing strength is less than 725 lbs. There is evidence at the 0.10 level of significance

Using a one-tailed test with a significance level of 0.10, we can determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative.

The null hypothesis can be stated as H₀: µ ≥ 725, and the alternative hypothesis can be stated as H₁: µ < 725.

To test this hypothesis, we can use a t-test with a t-statistic of:

t = ([tex]\bar{X}[/tex] - µ₀) / (s / √n)

Where [tex]\bar{X}[/tex] is the sample mean, µ₀ is the null hypothesis mean (725 lbs.), s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (720 - 725) / (20 / √50) = -1.77

Using 49 degrees of freedom (n-1), at a significance level of 0.10 and a one-tailed test, the critical t-value is -1.645. Since our calculated t-value (-1.77) is less than the critical t-value, we can reject the null hypothesis in favor of the alternative.

This means that there is evidence at the 0.10 level of significance that the mean shearing strength of the rivets is below 725 lbs.

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the probability of blindly drawing at least one blue marble in two attempts from the given bag of marbles is 1/2 or 50%.

To calculate the probability of drawing at least one blue marble in two attempts from a bag containing one blue, one green, one orange, and one yellow marble, we need to consider the possible outcomes.

In the first attempt, there are four marbles in the bag, and one of them is blue. So, the probability of drawing a blue marble on the first attempt is 1/4.

In the second attempt, if a blue marble was not drawn in the first attempt, there will be three marbles left in the bag, and one of them is blue. The probability of drawing a blue marble on the second attempt, given that a blue marble was not drawn in the first attempt, is 1/3.

To find the probability of drawing at least one blue marble, we can calculate the probability of the complement event (not drawing a blue marble in both attempts) and subtract it from 1:

Probability of drawing at least one blue marble = 1 - Probability of not drawing a blue marble in both attempts

Probability of not drawing a blue marble in both attempts = (3/4) * (2/3) = 1/2

Probability of drawing at least one blue marble = 1/2 or 50%.

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Answer:

-4

Step-by-step explanation:

H=4x-4

4x-4(4) write into equation

4x-16 multiply the fours

x=-4 divide both sides by four and you get your answer

In terms of probability, we can say that the probability of selecting a coffee maker with a defective cord is 5.0% or 0.05. The percentage of coffee makers with a defective cord.

To find the probability of a coffee maker having a defective cord, we'll use the given information about faulty switches and defective cords.

We know that:
1. 6.0% of coffee makers have either a faulty switch or a defective cord.
2. 1.5% have a faulty switch.
3. 0.5% have both defects.

Using the formula for the probability of the union of two events (A or B) - P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A represents the event of a faulty switch, B represents the event of a defective cord, and A ∩ B represents both defects:

P(A ∪ B) = 6.0% (either a faulty switch or a defective cord)
P(A) = 1.5% (faulty switch)
P(A ∩ B) = 0.5% (both defects)

We need to find P(B), the probability of a coffee maker having a defective cord.

Using the formula, we can write:
6.0% = 1.5% + P(B) - 0.5%

Now, we'll solve for P(B):
6.0% = 1.0% + P(B)
P(B) = 6.0% - 1.0%
P(B) = 5.0%

Therefore, the probability (percent) of a coffee maker having a defective cord is 5.0%.

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There are 43,200 number of ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

To find the number of ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order, follow these steps:

1. Identify the vowels and consonants: Vowels are U, I, E, A, and Y; consonants are N, R, S, S, L, and L.

2. Arrange the consonants in alphabetical order: L, L, N, R, S, S.

3. Count the number of positions available for placing the vowels: There are 7 positions available for the vowels (between the consonants and at the beginning and the end of the word), which are _ L _ L _ N _ R _ S _ S _.

4. Count the permutations of the vowels: There are 5 vowels with the letters U, I, E, A, and Y occurring once. So there are 5! = 120 permutations.

5. Consider the consonants with repeating letters: Since there are two Ls and two Ss, we must divide the total permutations by the product of the repetitions (2! for L and 2! for S). Therefore, there are 6!/(2!*2!) = 360 arrangements for consonants.

6. Combine the permutations of vowels and consonants: To find the total number of ways to arrange the letters, multiply the permutations of vowels (120) by the arrangements for consonants (360).

120 * 360 = 43,200

So, there are 43,200 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

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If the sampled points are spatially correlated in kriging, then one would expect an increase in the semivariance with an increase in the distance between sampled points.

Step-by-step explanation:

1. Kriging is a geostatistical interpolation technique used to estimate values at unsampled locations based on sampled data points.
2. Spatial correlation refers to the relationship between values at different locations in space.
3. Semivariance is a measure of how much the values at different locations vary, and it is used to quantify the spatial correlation in kriging.
4. When the sampled points are spatially correlated, the semivariance will generally increase as the distance between sampled points increases.
5. This increase in semivariance with distance is due to the fact that points that are farther apart are less likely to have similar values than points that are closer together.

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The natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

To find the natural values of n for which the difference (2-2n) - (5n-27) is positive, we need to simplify the expression and then solve for n.

(2-2n) - (5n-27) = 2 - 2n - 5n + 27

= -7n + 29

So, we need to find the natural numbers n for which -7n + 29 > 0.

To do this, we can solve for n as follows

-7n + 29 > 0

-7n > -29

n < 29/7

Since n is a natural number, it must be an integer greater than or equal to 1. Therefore, the natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

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Significant correlations are useful statistical tools for identifying relationships between variables, but they are not able to indicate causality.

While they can demonstrate the strength of the effect through the correlation coefficient, the size of the effect by examining the magnitude of the relationship, and the probability level by evaluating the likelihood that the observed relationship occurred by chance, they cannot prove that one variable directly causes changes in another variable.

Correlations can only show that two variables are related, but they do not provide information about the nature of that relationship. It is important to remember that correlation does not imply causation. There might be other factors, known as confounding variables, that affect both variables and create the appearance of a relationship where none truly exists.

To determine causality, researchers must conduct controlled experiments where they manipulate the independent variable and observe the effect on the dependent variable, while holding all other factors constant. This allows them to isolate the cause-and-effect relationship between the two variables and draw more accurate conclusions.

In summary, while significant correlations can provide valuable information about the strength, size, and probability level of the relationship between variables, they cannot establish causality. To determine if one variable truly causes changes in another, controlled experiments must be conducted.

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Therefore, It will take approximately 5.68 hours for the colony of cells to reach 500, based on the given exponential equation.

In order to find out how many hours it will take for the colony of cells to reach 500, we can set up an exponential equation. Let's call the number of hours it takes for the colony to reach 500 "x". Using the information given in the problem, we know that the number of cells in the colony can be represented by the equation 10 * 3^x = 500.
To solve for x, we can divide both sides by 10 and take the logarithm of both sides. This gives us x = log(500/10) / log(3) ≈ 5.68 hours. Therefore, it will take approximately 5.68 hours for the colony of cells to reach 500.
Therefore, It will take approximately 5.68 hours for the colony of cells to reach 500, based on the given exponential equation.

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The confidence level for the given interval of 13.45 to 14.15 days is 95%, which means that we can be 95% confident that the true mean survival time falls within this range.

Based on the given information, we know that a random sample of 25 rats exposed to 10Sv of radiation has a mean lifetime of x=13.8 days. We also know that the LD100 is 14 days, and that the lifetimes for this level of exposure follow a normal distribution with unknown mean and standard deviation 0.75.

The report states that a confidence interval for the true mean survival time extends from 13.45 to 14.15 days, which means that we can be 95% confident that the true mean survival time falls within this range. This is because the confidence level for this interval is 95%.

To calculate this, we can use the formula:

Confidence level = 1 - alpha

where alpha is the significance level, which is typically set to 0.05 for a 95% confidence level. This means that there is a 5% chance that the true mean survival time is outside the given interval.

In conclusion, the confidence level for the given interval of 13.45 to 14.15 days is 95%, which means that we can be 95% confident that the true mean survival time falls within this range.

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Answer:

I hope this helps !

Step-by-step explanation:

Answer: False, normal distribution describes continuous random variables and not discrete random variables

Step-by-step explanation: To describe discrete random variables other patterns of distributions can be used like binomial distribution. Therefore it is not recommended to use normal distribution for them.

Although in rare cases values of discrete variables can be approximated via normal distribution too but these won't be accurate values hence highly unstable.

The value of given expression 1/5/14/3 of 10/7×14/5 is 6/35 with the help of PEMDAS rule.

PEMDAS is a commonly used acronym in mathematics that stands for "Brackets, Orders, Division, Multiplication, Addition, Subtraction." It is a rule that helps you remember the order of operations to solve mathematical expressions.

Use PEMDAS rule to solve the given expression

1/5/14/3 of 10/7 × 14/5

= 1/5/14/3 × 10/7 ×14/5

= 1/5 × 3/14 × 10/7 × 14/5

Cancelling the same terms and factors

= 1/5 × 3/1 × 10/7 × 1/5

= 1/5 × 3/1 × 2/7

= 6/35

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