Question 1

Suppose the time (in minutes) it takes for a commuter to travel to work is normally distributed with a mean of 26.8 and a standard deviation of 17.1. What is the z-score for a commuter who takes 15 minutes to travel to work?

Accepted Answer

$$z = \frac{15 - 26.8}{17.1}$$

Question 2

A survey finds that the time spent in a supermarket is normally distributed with a mean of 47 minutes and a standard deviation of 12 minutes. What is the probability that a randomly selected shopper spends between 26 and 56 minutes in the store?

Accepted Answer

0.7333

Question 3

If the number of active physicians per state is normally distributed with a mean of 286 and a standard deviation of 57 (per 100,000 residents), what is the probability that a randomly selected state has fewer than 300 active physicians per 100,000 residents?

Accepted Answer

0.597

Question 4

Which of the following best describes the area under the normal curve between two values $$a$$ and $$b$$?

Accepted Answer

The probability that the random variable falls between $$a$$ and $$b$$

Question 5

A normal distribution has mean $$\mu = 47$$ and standard deviation $$\sigma = 12. $$What is the expected number of shoppers (out of 200) who spend more than 35 minutes in the store, given $$P(x \u003e 35) = 0.8413$$?

Accepted Answer

$$200 	imes 0.8413 = 168.26$$

Question 6

Which of the following statements about the standard normal distribution is TRUE?

Accepted Answer

It has a mean of 0 and a standard deviation of 1.

Question 7

If $$z = 1$$ for a value $$x in a $$normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$, which equation correctly relates $$x$$, $$\mu$$, and $$\sigma$$?

Accepted Answer

$$x = \mu + \sigma$$

Question 8

A random variable $$x is $$normally distributed with mean $$\mu$$ and standard deviation $$\sigma. $$Which formula is used to convert $$x to a $$standard normal variable $$z$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 9

If the probability that a worker travels less than 15 minutes to work is 0.2451, how would you interpret this probability in the context of 1,000 randomly selected workers?

Accepted Answer

About 245 workers are expected to travel less than 15 minutes to work.

Question 10

Which of the following is NOT a requirement for using the normal distribution to approximate probabilities?

Accepted Answer

The variable must be categorical.

Question 11

A state has 320 active physicians per 100,000 residents. If the national mean is 286 and the standard deviation is 57, what is the z-score for this state?

Accepted Answer

$$z = \frac{320 - 286}{57}$$

Question 12

Which of the following best explains why the area under the normal curve represents probability?

Accepted Answer

Because the total area under the curve is 1, representing all possible outcomes.

Question 13

If you use technology to find the probability that $$x \u003c 300$$ for a normal distribution with $$\mu = 286$$ and $$\sigma = 57$$, which values must you input?

Accepted Answer

Mean, standard deviation, and the x-value 300

Question 14

A normal distribution is transformed to a standard normal distribution. What happens to the area under the curve for any given interval?

Accepted Answer

It remains unchanged.

Question 15

Which of the following is a real-world example of a variable that is likely to be normally distributed?

Accepted Answer

Heights of adult humans in a population

Normal Probability Distributions: Finding Probabilities

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