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# Elementary Statistics: Quiz 6: The Normal Distribution

Summary: This module is a quiz containing 10 multiple choice questions covering topics related to the normal distribution. This module is part of a set of companion resources to Collaborative Statistics (col10522) by Barbara Illowsky and Susan Dean.

## Exercise 1

Given X ~ N (300, 15), find P(280 < X < 340).

• A. 0.2000
• B. 0.7460
• C. 0.9050
• D. 0.9999

## Exercise 2

Given X ~ N(300, 15), find the 70th percentile.

• A. 0.5244
• B. 210.00
• C. 307.87
• D. 324.96

## Exercise 3

Given X ~ N(300, 15), what can be said of the median?

• A. The mode = median and the mode = the mean.
• B. It is the same as the mode.
• C. It is less than the average.
• D. It is the same as the average.

## Exercise 4

Given X ~ N(300, 15), the area to the right of x = 330...

• A. is the same as the area to the right of z = 2.
• B. P(X > 330) is the same as the area to the right of z = 2 AND to the left of X = 270.
• C. is the same as the area to the left of x = 270.
• D. is the same as the area to the left of x = 330.

## Exercise 5

Given X ~ N(300, 15), find the Interquartile Range (IQR).

• A. 0.50
• B. 310.12
• C. 20.24
• D. 289.99

## Exercise 6

Given X ~ N(300, 15), find the z-score associated with x = 290.

• A. 15/10
• B. -10
• C. 10/15
• D. -10/15

## Exercise 7

For what do we use z-scores?

• A. Because of the use of technology, there is no longer any use for z-scores.
• B. to standardize scores from two or more different normal distributions so that we may compare the scores.
• C. to help us calculate uniform and exponential probabilities.
• D. to make our calculations easier because the mean = 0.

## Exercise 8

Given that X ~ N(10, 2), X > 20...

• A. cannot happen.
• B. can happen 1/5 of the time.
• C. is very unlikely to occur.
• D. we cannot determine its probability.

## Exercise 9

Given that X ~ N(10, 2) and Y follows the Exponential Distribution with a mean of 10, which of the following are correct?

• A. The median for Y is greater than the median for X.
• B. The median for Y is less than the median for X.
• C. The percentiles for X and Y are also equal.
• D. The median for X and Y are also equal.

## Exercise 10

For data that is normally distributed, is it possible for the standard deviation to be larger than the mean?

• A. No.
• B. Yes.
• C. There is not enough information to determine.

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