# Probability distribution | Mathematics homework help

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BUS210 Business Statistics

Directions: Answer the following exercises. Please show all of your work for each exercise.

Complete and submit the following problems from your text:

Chapter 6: Exercises #14 and #46

Chapter 7: Exercises #10, #38 and #52

**Chapter 6**

14. The United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different locations.

a. What is the probability that all six will arrive within two days?

b. What is the probability that exactly five arrive within two days?

c. Find the mean number of letters that will arrive within two days.

d. Compute the variance and standard deviation of the number that will arrive within two days.

46. Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 45 percent of college students watch soap operas during the afternoon. To further investigate, she selects a sample of 10.

a. Develop a probability distribution for the number of students in the sample who watch soap operas.

b. Find the mean and the standard deviation of this distribution.

c. What is the probability of finding exactly four watch soap operas?

d. What is the probability less than half of the students selected watch soap operas?

**Chapter 7**

10. The mean of a normal probability distribution is 60; the standard deviation is 5.

a. About what percent of the observations lie between 55 and 65?

b. About what percent of the observations lie between 50 and 70?

c. About what percent of the observations lie between 45 and 75?

38. A study of long distance phone calls made from the corporate offices of Pepsi Bottling Group, Inc., in Somers, New York, revealed the length of the calls, in minutes, follows the normal probability 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 communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time?

This is the end of Assignment 4.