Name:    AII.11 - Normal Distribution

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1

A normally distributed set of 968 values has a standard deviation of 11 and a mean of 108.  Which is closest to the number of values expected to be above 125?
 a. 910 c. 210 b. 989 d. 59

2

A population of adult males had their heights measured.  The heights were normally distributed. Approximately what percentage of heights, rounded to the nearest whole number, are within one standard deviation of the mean?
 a. 34% c. 68% b. 95% d. 99.7%

3

At a company, the data set containing the ages of applicants for a particular job was normally distributed.  The mean age of the applicants was 30 years old, and the standard deviation of the data set was 3.5 years.  Which is closest to the percent of applicants that were 21 years old or younger?
 a. 0.5% c. 2.57% b. 2.0% d. 9.0%

4

The normally distributed data set of 500 values has a mean of 35 and a standard deviation of 7.  Which is closest to the probability that a value in the data set will fall between 42 and 46?
 a. 0.04 c. 10 b. 0.1 d. 50

5

A normally distributed data set of 600 values has a mean of 18.5 and a standard deviation of 3.25.  Which is closest to the expected number of values in the data set that lie between 21 and 27?
 a. 6 c. 130 b. 22 d. 467

6

The useful life of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles.  What is the probability that if a radial tire is purchased at random, it will last between 20,000 and 35,000 miles?
 a. 94% b. 81% c. 68% d. 47%

7

The weights of eggs produced on a farm are normally distributed with a mean of 1.4 ounces and a standard deviation of 0.4 ounces.  To be graded extra large, an egg must weigh at least 2 ounces.  What is the probability that an egg from this farm will be graded extra large?
 a. 0.934 c. 0.066 b. 0.157 d. 0.025

8

For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time between charges will be between 50 and 70 hours.
 a. 0.9082 b. 0.8989 c. 0.5 d. 0.4082

9

In a city, it is estimated that the maximum temperature for the thirty days of June is normally distributed with a mean of 23 and a standard deviation of 5. Calculate the number of days in this month in which it is expected to reach a maximum temperature between 21 and 27.
 a. 4 days b. 8 days c. 10 days d. 13 days

10

The graph represents 500 college students whose mean weight is 70 kg with a standard deviation of 3 kg.

Identify the region(s) under the curve where only the weights of approximately 235 students are located.

 I.       p,r II.    q,s III.    r,s IV.    q,r V.    r,t VI.    s,t
 a. I, II, III b. I, IV, VI c. II, IV, V, VI d. II, III, IV, V

Numeric Response

11

Directions: Type your answer in the box.  Your answer must be in the form of an integer.

The heights of 200 kindergarten students at T. E. Wright Elementary are normally distributed with mean of 40 inches and a standard deviation of 1.8 inches.  Approximately how many students have a height between 37.3 inches and 44.5 inches?

12

The running times for a group of 200 runners to complete a one mile run are normally distributed with a mean of 6.5 minutes and a standard deviation of 1.5 minutes. Approximately how many of the runners have a time greater than 8 minutes?

13

The running times for a group of 200 runners to complete a one mile run are normally distributed with a mean of 6.5 minutes and a standard deviation of 1.5 minutes. What percentage, rounded to the nearest tenth, of these runners can complete this run in less than 3.5 minutes?

14

A normally distributed data set of 600 values has a mean of 18.5 and a standard deviation of 3.25.  What is the approximate number of values in the data set expected to be 22 or greater?

15

A normally distributed data set of 600 values has a mean of 18.5 and a standard deviation of 3.25.  What is the approximate number of values in the data set expected to be 16 or fewer?

16

A normally distributed data set of 600 values has a mean of 18.5 and a standard deviation of 3.25.  What is the approximate number of values in the data set expected to be 22 or greater?

17

Directions: Determine the letter of each region you want to select.  You may select more than one region.

The graph summarizes the test scores of 50,000 students.  The data is normally distributed with a mean of 81 and a standard deviation of 2.5.

Identify the regions under the curve where only the data for approximately 23,750 students are located.