Question 1

What is the term for the number of standard deviations an observation falls from the mean?

Accepted Answer

z score

Question 2

Given two normal curves, one with mean 23 and standard deviation 1, and another with mean 5 and standard deviation 10, which curve is more dispersed?

Accepted Answer

the second normal curve

Question 3

For a normal curve with mean 8 and standard deviation 7, which of the following intervals will define an area underneath the curve of approximately 0.68?

Accepted Answer

from 4.5 to 11.5

Question 4

Which graph represents a normal distribution with the largest standard deviation?

Accepted Answer

A

Question 5

Find the area under the standard normal curve to the left of $$z = -1.30.$$

Accepted Answer

0.0823

Question 6

Find the area under the standard normal curve to the right of $$z = 2.$$

Accepted Answer

0.1359

Question 7

Find the area under the standard normal curve to the left of $$z = 1.5.$$

Accepted Answer

0.9332

Question 8

Use the standard normal distribution to find $$P(2.25 \u003c z \u003c 0).$$

Accepted Answer

0.6831

Question 9

For the standard normal curve, find the $$z-$$score that corresponds to the third quartile.

Accepted Answer

0.77

Question 10

An airline knows from experience that the distribution of the number of suitcases lost each week on a certain route is approximately normal with $$\mu = 15.5$$ and $$\sigma = 3.6. $$What is the probability that during a given week the airline will lose less than 20 suitcases?

Accepted Answer

0.8944

Question 11

An airline knows from experience that the distribution of the number of suitcases lost each week on a certain route is approximately normal with $$\mu = 15.5$$ and $$\sigma = 3.6. $$What is the probability that during a given week the airline will lose between 10 and 20 suitcases?

Accepted Answer

0.4040

Question 12

Assume the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percent of men meeting these height requirements.

Accepted Answer

96.26\%

Question 13

A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3,000 miles. If the manufacturer is willing to replace no more than 10\% of the tires, what should be the approximate number of miles for a warranty?

Accepted Answer

43,660

Question 14

The probability distribution of the sample mean is called the:

Accepted Answer

sampling distribution of the mean

Question 15

As the sample size becomes large, the sampling distribution of the sample mean approaches a:

Accepted Answer

the sample size is 30 or more

Question 16

Which of the following statements explains the following graphic, which includes a picture of a distribution along with three sampling distributions of the mean with different sample sizes?

Accepted Answer

Averages calculated from larger samples will be less variable.

Question 17

If the standard deviation of a population is 20 and we take a sample of size 16 from which to calculate a mean, the standard error (the standard deviation of the sample mean) is:

Accepted Answer

5

Question 18

Assume the mean number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds. If a sample of 100 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds.

Accepted Answer

0.0885

Question 19

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $$32,000$$ and a standard deviation of $$3500. If 100 $$teachers are randomly selected, find the probability that their mean salary is greater than $$32,500.$$

Accepted Answer

0.1312

Question 20

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds. If a sample of 100 individuals is randomly selected, find the probability that the mean of the sample will be greater than 200 pounds.

Accepted Answer

0.7613

Normal Distributions, Z-Scores, and Sampling Distributions: Study Notes

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