Introduction to Normal Distributions Answers

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?

The lengths of a lawn mower part are approximately normally distributed with a given mean = 4 in. and standard deviation = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.?

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?

The graph below shows three different normal distributions.Which statement must be true?

The set of life spans of an appliance is normally distributed with a mean = 48 months and a standard deviation = 8 months. What is the z-score of an appliance that stopped working at 64 months?

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?

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?

The lengths of a lawn mower part are approximately normally distributed with a given mean = 4 in. and standard deviation = 0.2 in. What percentage of the parts will have lengths between 3.8 in. and 4.2 in.?

The class scores of a history test have a normal distribution with a mean = 79 and a standard deviation = 7. If Opal’s test score was 72, which expression would she write to find the z-score of her test score?

The weights of boxes of candies produced in a factory are normally distributed with a mean weight of 16 oz and a standard deviation of 1 oz. What is the weight of a box of candies with a z-score of 2?

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?

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?

The set of life spans of an appliance is normally distributed with a mean = 48 months and a standard deviation = 8 months. What is the z-score of an appliance that stopped working at 64 months?

What is the mean of the normal distribution shown below?

The graph below shows three different normal distributions.Which statement must be true?