# Binomial Probability

Chapter 05

57.) There are 10 homes constructed in Quail Creek area and 4 include Security systems. Three homes are selected at random:

a.) What is the probability all three of the selected homes have a security system?

b.) What is the probability that none of the three selected homes have a security system?

c.) What is the probability at least one of the selected homes have a security system?

d.) Did you assume the events to be dependent or independent?

59.) The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom are women. A new policy and procedure manual is to be written for the company.

a.) What is the probability that all members of the committee are men?

b.) What is the probability that at least 1 member of the committee is a woman?

Chapter 06

44.) The Bank of Hawaii reports that 7% of its credit card holders will default at some time in their life. The Hilo branch just mailed out 12 new cards today.

a.) How many of these new card holders would you expect to default? What is the standard deviation?

b.) What is the likelihood that none of the cardholders will default?

c.) What is the likelihood that at least one will default?

46.) Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 45% 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?

47.) A recent study conducted by Penn, Shone, and Borland, on behalf of LastMinute.com, revealed that 52% of business travelers plan their trips less than two weeks before departure. The study is to be replicated in the tri-state area with a sample of 12 frequent business travelers.

a.) Develop a probability distribution for the number of travelers who plan their trips within two weeks of departure.

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

c.) What is the probability exactly 5 of the 12 selected business travelers plan their trips within two weeks of departure?

d.) What is the probability 5 or fewer of the 12 selected business travelers plan their trips within two weeks of departure?

#### Solution Summary

The solution provides step by step method for the calculation of binomial probabilities and mean and standard deviation of a binomial distribution. Formula for the calculation and Interpretations of the results are also included.