# Probability: Binomial & Poisson

1. A discrete random variable can have the values x =3

x=8, or x=10, and the respective probabilities are 0.2,

0.7, and 0.1. Determine the mean, variance, and standard

deviation of x.

2. According to the National Marine Manufacturers

Association, 50.0% of the population of Vermont were

boating participants during the most recent year. For a

randomly selected sample of 20 Vermont residents, with

the discrete random variable x = the number in the sample

who were boating participants that year, determine

the following:

a E = x b. P(x <or_8) c.P( x = 10)

d. P( x = 12) e. P( 7 < or _ x < or _ 13)

3. It has been estimated that one in five Americans suffers

from allergies. The president of Hargrove University

plans to randomly select 10 students from the undergraduate

population of 1400 to attend a dinner at his home.

Assuming that Hargrove students are typical in terms of

susceptibility to allergies and that the college president's

home happens to contain just about every common allergen

to which afflicted persons react, what is the probability

that at least 8 of the students will be able to stay for

the duration of the dinner event?

4. According to the Mortgage Bankers Association of

America, the foreclosure rate on home mortgages in 2001

was 1%. Assuming that this rate is applicable to a

community where 1000 homes have mortgages, use the

Poisson approximation to the binomial distribution to

determine the following for x = the number of

foreclosures in this community during the coming year:

a. E(x)

b. P( x = 7)

c. P( x = 10)

d. P( 8 <or_ x <or_15)

#### Solution Summary

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