Q: A test score is normally distributed with a mean of 80 and a standard deviation of 6. What is the 90th percentile score?

Find $$z$$ for 0.90: $$z = 1.28$$. $$X = 80 + 1.28 \times 6 = 87.68$$

Question 1

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

Accepted Answer

The total area under the curve is 0.5.

Question 2

Suppose the heights of adult males are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the $$z-$$score for a man who is 76 inches tall?

Accepted Answer

$$z = \frac{76 - 70}{3} = 2$$

Question 3

If $$P(z \u003c a) = 0.9750$$ for a standard normal distribution, what is the value of $$a$$?

Accepted Answer

$$a = 1.96$$

Question 4

A bone density test result is normally distributed with a mean of 0 and a standard deviation of 1. If a patient’s $$z-$$score is $$-1.27$$, what is the probability that a randomly selected result is less than $$-1.27$$?

Accepted Answer

$$P(z \u003c -1.27) = 0.1020$$

Question 5

Which of the following best describes the relationship between area and probability in the context of the standard normal distribution?

Accepted Answer

The area under the curve to the left of a $$z-$$score represents the probability that a value is less than that $$z-$$score.

Question 6

A vehicle speed at a highway location is normally distributed with a mean of 65 mph and a standard deviation of 5 mph. What is the probability that a randomly selected vehicle will be traveling between 60 mph and 73 mph?

Accepted Answer

Find $$z-$$scores: $$z_1$$ = \frac{60-65}{5} = -1$$, z_2$ = \frac{73-65}{5} = 1.6$$. $$P(-1 \u003c z \u003c 1.6) = 0.9452 - 0.1587 = 0.7865$$

Question 7

Given a standard normal distribution, what is the probability that $$z is $$greater than 2.00?

Accepted Answer

$$P(z \u003e 2.00) = 1 - 0.9772 = 0.0228$$

Question 8

If the area to the left of a $$z-$$score is 0.8413, what is the value of the $$z-$$score?

Accepted Answer

$$z = 1.00$$

Question 9

Which of the following steps is NOT part of the procedure for finding areas (probabilities) with a non-standard normal distribution?

Accepted Answer

Multiply the $$z-$$score by the mean.

Question 10

A test score is normally distributed with a mean of 80 and a standard deviation of 6. What is the 90th percentile score?

Accepted Answer

Find $$z$$ for 0.90: $$z = 1.28$$. $$X = 80 + 1.28 	imes 6 = 87.68$$

Question 11

If $$P(z \u003c a) = 0.25$$ for a standard normal distribution, what is the value of $$a$$?

Accepted Answer

$$a = -0.674$$

Question 12

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

The curve is skewed to the right.

Question 13

A researcher wants to find the probability that a randomly selected value from a normal distribution is between two values, $$a$$ and $$b. $$Which of the following is the correct approach?

Accepted Answer

Find the $$z-$$scores for $$a$$ and $$b$$, then subtract the area to the left of $$a$$ from the area to the left of $$b.$$

Question 14

If the probability of a value being less than $$z is 0.1587$$, what is the value of $$z$$?

Accepted Answer

$$z = -1.00$$

Question 15

Which of the following is the correct formula for converting a value $$x$$ from a normal distribution with mean $$\mu$$ and standard deviation $$\sigma to a$$ $$z-$$score?

Accepted Answer

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

Chapter 6: The Normal Distribution – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards