Question 1

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

Accepted Answer

It has a standard deviation of 2.

Question 2

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

Accepted Answer

0.8980

Question 3

For a uniform distribution over the interval $$[0, 5]$$, what is the probability that a randomly selected value is at least 2?

Accepted Answer

0.6

Question 4

Which formula gives the probability density function (pdf) of a normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 5

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

Accepted Answer

0.8413

Question 6

A continuous random variable $$X is $$uniformly distributed between 0 and 10. What is the height of the density curve?

Accepted Answer

0.1

Question 7

Which of the following statements about density curves is TRUE?

Accepted Answer

The total area under any density curve is always equal to 1.

Question 8

Given a standard normal distribution, what is the area between $$z = -1.00$$ and $$z = -2.50$$?

Accepted Answer

0.1525

Question 9

In the context of normal distributions, what does the notation $$P(a \u003c z \u003c b)$$ represent?

Accepted Answer

The probability that the $$z-$$score is between $$a$$ and $$b.$$

Question 10

A critical value $$z_{\alpha} is $$defined as:

Accepted Answer

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

Question 11

If you want to find the $$z-$$score such that 2.5% of the area is to its right, which value do you use?

Accepted Answer

$$z_{0.025} = 1.96$$

Question 12

A hospital records the waiting times at a security checkpoint as uniformly distributed between 0 and 5 minutes. What is the probability that a randomly selected person waits less than 3 minutes?

Accepted Answer

0.6

Question 13

Which of the following best describes a uniform distribution?

Accepted Answer

A distribution where all values in the range are equally likely.

Question 14

If the area to the left of $$z = 1.27 is 0.8980$$, what percentage of people have a $$z-$$score above 1.27?

Accepted Answer

10.20%

Question 15

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

Question 16

A continuous random variable $$X$$ has a uniform distribution on $$[a, b]. $$What is the formula for the probability that $$X$$ falls between $$c$$ and $$d$$ ($$a \leq c \u003c d \leq b$$)?

Accepted Answer

$$P(c \u003c X \u003c d) = \dfrac{d-c}{b-a}$$

Question 17

If a normal distribution has mean $$\mu$$ and standard deviation $$\sigma$$, what is the $$z-$$score for a value $$x$$?

Accepted Answer

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

Question 18

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 large population.

Question 19

If you are given a cumulative area (probability) and need to find the corresponding $$z-$$score, what is the correct approach using Table A-2?

Accepted Answer

Locate the closest probability in the body of the table and identify the corresponding $$z-$$score.

Normal Probability Distributions: Key Concepts and Applications

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