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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.