Question 1

Which of the following equations represents the probability density function of a normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 2

A standard normal distribution has which of the following properties?

Accepted Answer

Mean $$\mu = 0$$ and standard deviation $$\sigma = 1$$

Question 3

The area under the entire density curve of any continuous probability distribution is always:

Accepted Answer

$$1$$

Question 4

If waiting times at an airport security checkpoint 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 5

For a uniform distribution on the interval $$[a, b]$$, what is the height of the density function?

Accepted Answer

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

Question 6

Which of the following best describes the shape of a normal distribution?

Accepted Answer

Bell-shaped and symmetric

Question 7

Given a standard normal distribution, what is the probability that a randomly selected z-score is less than 1.27?

Accepted Answer

$$0.8980$$

Question 8

If the area to the left of $$z = -1.00 is$$ $$0.1587$$, what is the probability that a randomly selected z-score is greater than $$-1.00$$?

Accepted Answer

$$0.8413$$

Question 9

A bone density reading between $$z = -1.00$$ and $$z = -2.50 is $$considered osteopenia. What is the probability that a randomly selected subject has a reading in this range?

Accepted Answer

$$0.1525$$

Question 10

Which notation represents the probability that a z-score is between $$a$$ and $$b$$?

Accepted Answer

$$P(a \u003c z \u003c b)$$

Question 11

If you want to find the z-score with an area of $$\alpha to $$its right in the standard normal distribution, which notation is used?

Accepted Answer

$$z_{\alpha}$$

Question 12

To find the value of $$z_{0.025}$$, which cumulative area from the left should you use?

Accepted Answer

$$0.975$$

Question 13

Which Excel function would you use to find the cumulative area to the left of a z-score in the standard normal distribution?

Accepted Answer

NORM.S.DIST

Question 14

A continuous random variable $$X is $$uniformly distributed on $$[0, 5]. $$What is the probability that $$X is $$between 1 and 4?

Accepted Answer

$$0.6$$

Question 15

If the area to the left of $$z = 1.00 is$$ $$0.8413$$, what is the probability that a randomly selected z-score is greater than $$1.00$$?

Accepted Answer

$$0.1587$$

Question 16

Which of the following statements is TRUE about the relationship between area and probability in a density curve?

Accepted Answer

The area under the curve for a given interval equals the probability of the variable falling within that interval.

Question 17

A critical value $$z_{0.05} is $$needed for a hypothesis test. What cumulative area from the left should you use to find this value?

Accepted Answer

$$0.95$$

Question 18

If a normal distribution has $$\mu = 10$$ and $$\sigma = 2$$, what is the z-score for $$x = 14$$?

Accepted Answer

$$2$$

Question 19

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

Accepted Answer

It is skewed to the right.

Question 20

A hospital uses z-scores to interpret bone density tests. If a patient's z-score is $$-2.5$$, what does this indicate about their bone density compared to the population mean?

Accepted Answer

Their bone density is 2.5 standard deviations below the mean.

Normal and Uniform Probability Distributions: Concepts, Calculations, and Applications

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