STAT Question 1-9
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stat_questions.docx1.
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The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of Mercury. The systolic blood pressures of four adults selected at random are 121 millimeters of mercury, 113 millimeters of mercury, 106 millimeters of mercury, and 127 millimeters of mercury. The graph of the standard normal distribution is shown to the right. Complete parts (a) through (c) below. |
z |
(a) Without converting to z-scores, match the values with the letters A, B, C, and D on the given graph of the standard normal distribution.
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A=
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B= |
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C=
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D= |
(Type whole numbers.)
(b) Find the z-score that corresponds to each value and check your answers to part (a).
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zA= |
zB=
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zC=
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zD= |
(Round to two decimal places as needed.)
(c) Determine whether any of the values are unusual, and classify them as either unusual or very unusual. Select the correct answer below and, if necessary, fill in the answer box(es) within your choice.
A.
The unusual value(s) is/are __. The very unusual value(s) is/are ___.
(Use a comma to separate answers as needed.)
B.
The very unusual value(s) is/are ___. The unusual values are all very unusual.
(Use a comma to separate answers as needed.)
C.
The unusual value(s) is/are __.There are no very unusual values.
(Use a comma to separate answers as needed.)
D.
There are no unusual or very unusual values.
2. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 67.1 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (c).
(a) Find the probability that his height is less than 66 inches.
The probability that the study participant selected at random is less than 66 inches tall is ___.
(Round to four decimal places as needed.)
(b) Find the probability that his height is between 66 and 71 inches.
The probability that the study participant selected at random is between 66 and 71 inches tall is ___.
(Round to four decimal places as needed.)
(c) Find the probability that his height is more than 71 inches.
The probability that the study participant selected at random is more than 70 inches tall is ___
(Round to four decimal places as needed.)
3.
The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 200 milligrams per deciliter and a standard deviation of 38.6 milligrams per deciliter.
(a) What percent of the men have a total cholesterol level less than
223 milligrams per deciliter of blood?
(b) If 245 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than
264 milligrams per deciliter of blood?
_________________________________________________________
(a) The percent of the men that have a total cholesterol level less than
233 milligrams per deciliter of blood is__ %
(Round to two decimal places as needed.)
(b) Of the 245 men selected, __ would be expected to have a total cholesterol level greater than 264 milligrams per deciliter of blood.
(Round to the nearest integer as needed.)
4.
In a survey of women in a certain country (ages 20−29), the mean height was 64.1 inches with a standard deviation of 2.91 inches. Answer the following questions about the specified normal distribution.
(a) What height represents the 90th percentile?
(b) What height represents the first quartile?
(a) The height that represents the 90th percentile is __ inches.
(Round to two decimal places as needed.)
(b) The height that represents the first quartile is __ inches.
(Round to two decimal places as needed.)
5.
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The time spent (in days) waiting for a heart transplant in two states for patients with type A+ blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts (a) and (b) below.
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(a) What is the shortest time spent waiting for a heart that would still place a patient in the top 5% of waiting times? __ days
(Round to two decimal places as needed.)
(b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 15% of waiting times? ___ days (Round to two decimal places as needed.)
6.
A population has a mean μ= 75 and a standard deviation σ= 28. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=261.
μ-x=___
(Simplify your answer.)
σ-x= ___
(Type an integer or decimal rounded to three decimal places as needed.)
7.
Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.
The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 103 pounds and a standard deviation of 39.9 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined.
μ-x= ___
σ-x=___
(Round to three decimal places as needed.)
Sketch a graph of the sampling distribution. Choose the correct graph below.
8. The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.8 hours and a standard deviation 0.33 hour. Random samples of size 22 and 35 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases?
If the sample size is n=22, find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is __
(Type an integer or a decimal.)
The standard deviation of the distribution of sample means is ___
(Round to two decimal places as needed.)
If the sample size is n=35, find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is __
(Type an integer or a decimal.)
The standard deviation of the distribution of sample means is ___
(Type an integer or decimal rounded to the nearest hundredth as needed.)
What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases? Choose the correct answer below.
A.
The mean and the standard deviation both decrease.
B.
The mean stays the same, but the standard deviation increases.
C.
The mean stays the same, but the standard deviation decreases.
Your answer is correct.
D.
The mean and the standard deviation both increase.
9.
Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability.
The probability that the mean price per gallon is less than $2.822 is __
(Round to four decimal places as needed.)
