Question 1

Given a normal distribution, if you are told that 55% of the distribution's area lies to the left of a certain value, what is the corresponding z-score? Use the provided z-table image.

Accepted Answer

$$z = 0.13$$

Question 2

A hospital administrator wants to know the minimum number of hours a medical resident must sleep to be in the top 5% of sleepers, given that the mean sleep time is $$\mu = 6.1$$ hours and the standard deviation is $$\sigma = 1.0$$ hour. What is the minimum sleep time?

Accepted Answer

$$x = 7.745$$ hours

Question 3

Which of the following formulas is used to convert a z-score to an x-value in a normal distribution?

Accepted Answer

$$x = \mu + z \cdot \sigma$$

Question 4

If you are given a percentile (such as the 90th percentile) and asked to find the corresponding x-value in a normal distribution, what is the correct sequence of steps?

Accepted Answer

Convert percentile to area, find closest z-score, then use $$x = \mu + z \cdot \sigma$$

Question 5

A survey of men aged 20–29 finds a mean height of $$\mu = 69.9$$ inches and a standard deviation of $$\sigma = 3.0$$ inches. What height represents the first quartile?

Accepted Answer

$$67.89$$ inches

Question 6

If you are asked to find the z-score for which 99% of the distribution’s area lies between $$-z$$ and $$z$$, what is the correct value?

Accepted Answer

$$z = \pm 2.575$$

Question 7

Which of the following best describes the process for finding a z-score given a percentile that is not exactly in the z-table?

Accepted Answer

Find the two closest areas in the table, choose the z-score with the smallest difference to the desired area

Question 8

A student finds that the area to the right of a certain z-score is 0.1190. What is the z-score?

Accepted Answer

$$z = 1.18$$

Question 9

If the area you are looking for is exactly halfway between two values in the z-table, what should you do?

Accepted Answer

Average the two corresponding z-scores

Question 10

Which of the following images best represents the area for the 90th percentile in a standard normal distribution?

Accepted Answer

The first image (area to the left of a positive z-score)

Question 11

A researcher wants to find the z-score that corresponds to the 5th percentile. What is the correct z-score?

Accepted Answer

$$z = -1.645$$

Question 12

If you are given a probability and asked to find the corresponding x-value in a normal distribution, which formula should you use after finding the z-score?

Accepted Answer

$$x = \mu + z \cdot \sigma$$

Question 13

Which of the following statements is TRUE regarding the use of the z-table?

Accepted Answer

Areas less than or equal to 0.5000 are found on the first page and correspond to negative z-scores

Question 14

A value is at the 78.5th percentile in a normal distribution. What is the corresponding z-score?

Accepted Answer

$$z = 0.79$$

Question 15

If you are asked to find the z-score for the first quartile, what area should you use?

Accepted Answer

$$0.2500$$

5.3

Study Guide - Practice Questions

Study Guide - Flashcards