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Elementary Statistics: Quiz 6: The Normal Distribution

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

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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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