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# Long distance calling and food expenditures based on a normal distribution

Problem 1
A recent report in USA Today indicated a typical family of four spends \$490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a mean of \$490 and a standard deviation of \$90.
a. What percent of the families spend more than \$30 but less than \$490 per month on food?
b. What percent of the families spend less than \$430 per month on food?
c. What percent spend between \$430 and \$600 per month on food?

Problem 2

A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group, Inc., in Somers, New York, showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes.
a. What fraction of the calls last between 4.2 and 5 minutes?
b. What fraction of the calls last more than 5 minutes?
c. What fraction of the calls last between 5 and 6 minutes?
d. What fraction of the calls last between 4 and 6 minutes?
e. As part of her report to the president, the Director of Communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time?

#### Solution Summary

Assuming a normal distribution, this solution calculates the probability/percent of food expenditures and long distance calling.

\$2.19