Question 1

Which of the following is NOT a property of the standard normal distribution?

Accepted Answer

It is skewed to the right.

Question 2

A continuous random variable $$X is $$uniformly distributed between $$a$$ and $$b. $$What is the formula for the height of its density curve?

Accepted Answer

$$\frac{1}{b-a}$$

Question 3

At JFK airport, waiting times at security are uniformly distributed between 0 and 5 minutes. What is the probability that a randomly selected passenger waits at least 2 minutes?

Accepted Answer

0.6

Question 4

Which equation represents the normal distribution probability density function?

Accepted Answer

$$y = \frac{e$$^{-\frac{1}$${2} \left( \frac{x-\mu}{\sigma} \$$right)^2$$}}{\sigma \sqrt{2\pi}}$$

Question 5

A bone density test score is normally distributed with mean 0 and standard deviation 1. What is the probability that a randomly selected person has a score less than 1.27?

Accepted Answer

0.8980

Question 6

For a standard normal distribution, what does the notation $$z_{\alpha}$$ represent?

Accepted Answer

The z-score with an area of $$\alpha to $$its right.

Question 7

If the area to the left of $$z = -1.00 is 0.1587$$, what is the probability that a randomly selected person has a bone density score above $$-1.00$$?

Accepted Answer

0.8413

Question 8

A bone density reading between $$z = -1.00$$ and $$z = -2.50$$ indicates osteopenia. If the area to the left of $$z = -1.00 is 0.1587 $$and to the left of $$z = -2.50 is 0.0062$$, what is the probability that a randomly selected person has osteopenia?

Accepted Answer

0.1525

Question 9

Which of the following statements about density curves is TRUE?

Accepted Answer

The total area under any density curve is exactly 1.

Question 10

Given a uniform distribution for waiting times between 0 and 5 minutes, what is the probability that a randomly selected passenger waits less than 3 minutes?

Accepted Answer

0.4

Question 11

Which of the following best describes a uniform distribution?

Accepted Answer

All values within the range are equally likely.

Question 12

If you want to find the probability that a standard normal variable $$z is $$greater than a given value $$a$$, which area do you use?

Accepted Answer

The area to the right of $$z = a$$ under the curve.

Question 13

Which of the following is the correct method to find the area between two z-scores $$a$$ and $$b$$ ($$a \u003c b) in $$the standard normal distribution?

Accepted Answer

Subtract the cumulative area to the left of $$a$$ from the cumulative area to the left of $$b.$$

Question 14

A critical value in the standard normal distribution is best described as:

Accepted Answer

A z-score on the borderline separating significantly low or high values.

Question 15

If you are given a cumulative area from the left of 0.975 in the standard normal distribution, what is the corresponding z-score?

Accepted Answer

1.96

Question 16

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.

Question 17

If the area to the left of $$z = 2.50 is 0.9938$$, what is the probability that $$z \u003e 2.50$$?

Accepted Answer

0.0062

Question 18

Which technology or tool is recommended for finding areas (probabilities) under the standard normal curve?

Accepted Answer

StatCrunch or calculators/software.

Question 19

What is the main difference between a normal and a uniform distribution?

Accepted Answer

Normal distribution is bell-shaped and symmetric; uniform distribution is rectangular and all values are equally likely.

Question 20

If you want to find the z-score corresponding to a cumulative area of 0.9 to the left, which value should you use?

Accepted Answer

The z-score with 0.9 area to its left, found in Table A-2 or using NORM.INV.

Normal and Uniform Probability Distributions: Concepts and Applications

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