# Using the normal distribution for determining probabilities

Continuous Probability Distributions

# 42

The accounting department at Weston Materials, Inc., a national manufacturer of unattached

garages, reports that it takes two construction workers a mean of 32 hours and

a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times

follow the normal distribution.

a. Determine the z values for 29 and 34 hours. What percent of the garages take between

32 hours and 34 hours to erect?

b. What percent of the garages take between 29 hours and 34 hours to erect?

c. What percent of the garages take 28.7 hours or less to erect?

d. Of the garages, 5 percent take how many hours or more to erect?

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# 45

Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the

human resource director shows the annual cost per employee per year followed the normal

probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.

a. What fraction of the employees cost more than $1,500 per year for dental expenses?

b. What fraction of the employees cost between $1,500 and $2,000 per year?

c. Estimate the percent that did not have any dental expense.

d. What was the cost for the 10 percent of employees who incurred the highest dental

expense?

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The solution provides guidelines and steps for determining the probability, of events, through the use of the normal distribution.