Introduction to Normal Distributions

Question 1

The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard deviation of $4,000. What is the z-score of a company employee who makes an annual salary of $54,000?

Revolt · Accepted Answer

D: 5

Question 2

The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.The mean of the temperatures in the chart is 24° with standard deviation of 4°. How many years had temperatures within one standard deviation of the mean?

Revolt · Accepted Answer

B: 25

Question 3

What is the mean of the normal distribution shown below?

Revolt · Accepted Answer

C: 4

Question 4

The amount of daily time that teenagers spend on a brand A cell phone is normally distributed with a given mean = 2.5 hr and standard deviation = 0.6 hr. What percentage of the teenagers spend more than 3.1 hr?

Revolt · Accepted Answer

C: 16%

Question 5

The lengths of a certain species of fish are approximately normally distributed with a given mean and standard deviation . According to the Empirical Rule, what percentage of the fish will have lengths within 1 standard deviation of the mean?

Revolt · Accepted Answer

C: 68%

Question 6

The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean?

Revolt · Accepted Answer

C: 22°

Question 7

The heights of a certain type of tree are approximately normally distributed with a mean height = 5 ft and a standard deviation = 0.4 ft. Which statement must be true?

Revolt · Accepted Answer

D: A tree with a height of 6.2 ft is 3 standard deviations above the mean.

Question 8

The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is more than one standard deviation above the mean?

Revolt · Accepted Answer

C: 30°

Question 9

The graph below shows two normal distributions.What is the difference of the means of the distributions?

Revolt · Accepted Answer

A: 15

Question 10

The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean = 43.8 miles per gallon and standard deviation = 5.1 miles per gallon. What percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?

Revolt · Accepted Answer

A: 68%

Introduction to Normal Distributions Answers

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