Answer:If we compare the p value and the significance level assumed we see thatso we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can conclude that the true mean is not different from the specification at 1% of signficance.
Step-by-step explanation:
The machine is working properly based on the convincing evidence provided by the sample.
How to calculate the test statistics.For the null hypothesis, we would test that:
H0 : p = 2
For the alternate hypothesis, we would test that:
Ha > p = 2
In Mathematics, the test statistics of a given sample is calculated by using this formula:
[tex]Z=\frac{x\;-\;u}{\frac{\sigma}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the sample size.Substituting the given parameters into the formula, we have;
[tex]Z=\frac{2.024\;-\;2}{\frac{0.205}{\sqrt{200} } }\\\\Z=\frac{0.024}{\frac{0.205}{14.14} }\\\\Z=\frac{0.024}{0.0145 }[/tex]
Z = 1.66.
For the p-value:
P(Z > Zo) = P(Z > 1.66)
P(Z > 1.66) = P(Z < -1.66)
P(Z < -1.66) = 0.0485.
From the z-table, a z-score of 1.66 corresponds has a p-value of 0.0485. Therefore, the p-value for this test is 0.0485 < 2 while assuming a confidence level of 95%.
In conclusion, we fail to reject the null hypothesis because 0.0485 < 2.
Read more on null hypothesis here: https://brainly.com/question/14913351
Function Notation
If f(x) = -3x2 + 2x - 8, find each of the following:
f(-1)
f(0)
f(3)
f(1/3)
can someone please help?? i just got done with one ttm lesson and now i need help with this one! tysm to whoever helps.
Calculate the volume of this triangular prism?
Answer:
960 sq cm
Step-by-step explanation:
(16*12*10)/2
Helppppppppppppppppp
Answer:
3. y = -⅕x - 5
Step-by-step explanation:
The equation of straight line is given by the formula, y = mx + c
Where;
m is the slope.
x and y are the points.
c is the intercept.
Given the standard form equation;
x + 5y = -25
Rearranging the equation, we have;
5y = -x - 25
Dividing all through by 5, we have;
y = -⅕x - 5
Consider △BTW as pictured below.
Find W.
Answer:
m<W: 23
Step-by-step explanation:
8x - 9 + 30x - 4 + 13x - 11 = 180
51x - 24 = 180
51x = 204
x = 4
m<W:
8x - 9
8(4) - 9
32 - 9
23
Please help me with this
can yall help please
Step-by-step explanation:
I think your answer will be 15
The Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before-tax family income is $ 85,050. Suppose that 56% of the before-tax family incomes when the head of the household has a college degree are between $75,000 and $95,100 and that these incomes are normally distributed. What is the standard deviation of before-tax family incomes when the head of the household has a college degree
Answer:
The standard deviation is $13,052.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When the head of the household has a college degree, the mean before-tax family income is $ 85,050.
This means that [tex]\mu = 85,050[/tex]
Suppose that 56% of the before-tax family incomes when the head of the household has a college degree are between $75,000 and $95,100 and that these incomes are normally distributed.
They are equally as far from the mean, one above, and one below. This means that when [tex]X = 95100[/tex], Z has a pvalue of 0.5 + (0.56/2) = 0.78. So when X = 95100, Z = 0.77. We use this to find [tex]\sigma[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.77 = \frac{95100 - 85050}{\sigma}[/tex]
[tex]0.77\sigma = 10050[/tex]
[tex]\sigma = \frac{10050}{0.77}[/tex]
[tex]\sigma = 13052[/tex]
The standard deviation is $13,052.
What is the distance between (-2, -3) and (-4, 3)? Use the distance formula and show your work.
Answer:
D = 6.32
Step-by-step explanation:
-2 to -4 = 2
-3 to 3 = 6
D² = 2² + 6²
D² = 4 + 36 = 40
D = 6.32
three friends go to a book fair . alvin speends 2.60 . prabhjot spends 4 times as much as alvin . stephanie spends 3.45 less then prabhjot . how much does stephanie spends?
Answer:
6.95
Step-by-step explanation:
to find how much stephanie spends for first we will find how much probhjot spends and then subtract 3.45 dollars from that value alvin spends 2.60 dollars
prohbjot spends 4 times as much as alvin or
4× 2.60=10.4
so prohbjot spends 10.4 dollars
stephanie spends3.45 dollars less than prohbjot or
10.4 -3.45 =6.95
so stephanie spends 6.95 dollars
giving brainliest *easy*
An elevator has a placard stating that the maximum capacity is 1580 lb-10 passengers. So, 10 adult male passengers can have a mean weight of up to 1580/10 = 158 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 158 lb. (Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 35 lb.) Does this elevator appear to be safe?
Answer:
a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb
b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 35 lb.
This means that [tex]\mu = 160, \sigma = 35[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{35}{\sqrt{10}} = 11.07[/tex]
a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.
This is 1 subtracted by the pvalue of Z when X = 158. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 160}{11.07}[/tex]
[tex]Z = -0.18[/tex]
[tex]Z = -0.18[/tex] has a pvalue of 0.4286
1 - 0.4286 = 0.5714
0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.
b.) Does this elevator appear to be safe?
No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
Pete painted 4/5 of a rectangle green. He painted 1/8 of the same rectangle blue. Pete painted the rest the rectangle red. What fraction of the rectangle did Pete paint red? please explain!
Answer:
Step-by-zbastep explanation:
Recommendations
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Seventh grade
> L.8 Solve percent equations: word problems JS6
You have prizes to reveal!
Learn with an example
The city council voted on a new tax. 27 council members voted in favor of the tax. The
council has 90 members. What percentage of the council members voted in favor of the tax?
Write your answer using a percent sign (%).
Submit
Answer:
Step-by-step explanation:
27 ÷ 90 = 0.3 = 0.30 = 30%
I NEED HELP ASAP!!!!!!!!!
Answer:
a=81.0
there ya go
this year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year
a. 4.28%
b. 4.68%
c. 4.92%
d. 5.12%
Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. Complete the distributions.
A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
B. P(_____) = _______.
C. Find the 95th percentile for the mean time to complete one month's reviews.
D.The 95th Percentile =________.
Answer:
a) [tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]
b) The 95th percentile is 4.4935 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours.
This means that [tex]\mu = 4, \sigma = 1.2[/tex]
16 reviews.
This means that [tex]n = 16, s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
This is the pvalue of Z when X = 4.25 subtracted by the pvalue of Z when X = 3.5. So
X = 4.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.25 - 4}{0.3}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a pvalue of 0.7967
X = 3.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.5 - 4}{0.3}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a pvalue of 0.0475
0.7967 - 0.0475 = 0.7492
So
[tex]P(3.5 \leq X \leq 4.25) = 0.7492[/tex]
C. Find the 95th percentile for the mean time to complete one month's reviews.
This is X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.645 = \frac{X - 4}{0.3}[/tex]
[tex]X - 4 = 0.3*1.645[/tex]
[tex]X = 4.4935[/tex]
The 95th percentile is 4.4935 hours.
Alice and Finn roll two number cubes. Which of the following rules will make the game fair?
A) Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled.
B) Alice wins if a total of 7 is rolled. Finn wins if a total of 8 is rolled.
C) Alice wins if a total of 3 is rolled. Finn wins if a total of 10 is rolled.
D) Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.
Answer:
Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.
(8x + 11x) + (-7 - 18)
Answer:
19x - 25
steps:
(8x + 11x) + (-7 - 18)
19x + (-25)
positive x negative = negative
19x - 25
Answer:
19x - 25
Step-by-step explanation:
(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...
19x + (-7 - 18) <--------------- subtract the bold ones...
(19x) - 25 <-------------------- eliminate parenthases
19x - 25 <--------------------- solution...
Plzzz someone help me
What is the product of (x - 5) and (x - 4)? Use the model to find the result.
Answer:
x2 - 9x +20
Step-by-step explanation:
PLS HELP DUE SOON WILL MARK BRAINLIEST
A store owner asks each person to write "Yes" or "No" on a slip of paper as
they leave, secretly writing down whether they were happy with their
experience. At the end of the day, the owner selects 12 slips at random and
looks at them. These were the results:
yes, yes, yes, no, yes, no, yes, yes, no, yes, no, yes
Part 1: Estimate the proportion of all shoppers who were haphy with their
experience that day. Enter your response as a decimal.
The estimated proportion of all shoppers who were happy with their experience that day and said yes is 0.667.
What is random sample?Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.
A store owner asks each person to write "Yes" or "No" on a slip of paper as they leave, secretly writing down whether they were happy with their experience.
At the end of the day, the owner selects 12 slips at random and looks at them. These were the results:
yes, yes, yes, no, yes, no, yes, yes, no, yes, no, yes=12yes=8To estimate the proportion is the following formula:
[tex]p'=\dfrac{x}{n}[/tex]
Here, x is the number of success and n is the sample size. Here, the sample size is 12 and number of success (yes) is 8. Thus, the estimated proportion is:
[tex]p'=\dfrac{8}{12}\\p'=0.667[/tex]
Thus, the estimated proportion of all shoppers who were happy with their experience that day and said yes is 0.667.
Learn more about the random sample here;
https://brainly.com/question/17831271
#SPJ1
PLEASE HELP!!! WILL MARK BRAINLIEST!!! Answers only related to the question please!
Exponential functions have the form f(x)= b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?
Answer:
x is form
Step-by-step explanation:
A football team has 5 freshman, 8 sophomores, 11 juniors, and 16 seniors. If two are chosen at random to participate in the coin toss, what is the probability that both players chosen will be seniors?
Answer:
The probability percentage that both players will be seniors is 15.38%.
Step-by-step explanation:
Given that a football team has 5 freshman, 8 sophomores, 11 juniors, and 16 seniors, if two are chosen at random to participate in the coin toss, to determine what is the probability that both players chosen will be seniors the following calculation must be done:
5 + 8 + 11 + 16 = 40
16/40 = X
4/10 = X
0.4 = X
15/39 = X
5/13 = X
0.38 = X
0.4 x 0.38 = X
0.1538 = X
Thus, the probability percentage that both players will be seniors is 15.38%.
A circular pool has a diameter of 25 feet. A 2 foot-wide sidewalk borders the entire pool. What is the approximate circumference of the outside edge of the sidewalk
A. 91 feet
B. 85 feet
C. 50 Feet
D. 27 feet
I’ll mark brainalist + points for answer / explanation
Answer:
Step-by-step explanation:
(A) não tenho sertesa
Area: 28.67 sq m and the side is 4.7 m The missing side length is equal to:??? m
Answer:
6.1
Step-by-step explanation:
area =leanth x breath.
if one side=4.7,
then, missing length=area/given side
= 28.67/4.7
=6.1
pretty difficult for me at least
Answer:
Sales tax = $1.25
Total = $25+$1.25 = $26.25
Step-by-step explanation:
Tax = 0.05 x 25 = 1.25
Total = 1.25 + 25
Answer:
To calculate tip or tax, simply move the decimal place 2 to the right and multiply it by the price. For example, If you want to leave a 20% tip, multiply the cost by 0.20 to get the tip amount or multiply the cost by 1.20 to get the total
The sales tax is $1.25
The total price is $26.25
Fred and Ted are interested in the average height of NC State students. They randomly sample students from NC State and construct confidence intervals from their data. Fred sampled 121 students to construct his confidence interval. Ted sampled 144 students to construct his confidence interval; both create histograms for their data which have symmetric, unimodal, and roughly bell-shaped distributions. Which of the following is true about the margins of error for these experiments?
a. Fred's margin of error is larger than Ted's.
b. Ted's margin of error is larger than Fred's.
c. Fred and Ted have the same size margins of error.
d. We are unable to determine which margin of error is larger without knowing more about Fred and Ted's samples.
Answer:
a. Fred's margin of error is larger than Ted's.
Step-by-step explanation:
Margin of error of a confidence interval:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level(the higher the confidence level the larger the value of z) [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
From this, we have that:
A higher confidence level leads to a larger margin of error.
A larger sample size leads to a smaller margin of error.
In this question:
Same confidence level.
Fred's sample is smaller, so his margin of error will be larger.
The correct answer is given by option a.
For the same confidence level, Fred's sample is smaller, so hir margin of error will be larger. The correct option is A.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
Fred and Ted are interested in the average height of NC State students.
They randomly sample students from NC State and construct confidence intervals from their data.
Fred sampled 121 students to construct his confidence interval.
Ted sampled 144 students to construct his confidence interval.
The margin of error of a confidence interval
[tex]\rm M =z \dfrac{\sigma }{\sqrt{n}}[/tex]
Where z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation level and n is a sample size.
By the formula, we have
A higher confidence level leads to a larger margin of error.
A larger sample size leads to a small margin of error.
For the same confidence level, Fred's sample is smaller, so hir margin of error will be larger. The correct option is A.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
Helpp which one pleasee
Answer:
coefficient because they are not the same so they can not be constant because it is not the same in every week
Please help me with this
73
Step-by-step explanation:
I think that this is an isosceles triangle, and like since ST=SR
Therefore, m(<T) = m(<R)= 73