HELP!!!! *Discrete Probability Distributions* HELP!!!!!

Question

According to sales information in the first quarter of 2016, 2.7% of new vehicles sold in the United States were hybrids. This is down from 3.3% for the same period a year earlier. An analyst’s review of the data indicates that the reasons for the sales decline include the low price of gasoline and the higher price of a hybrid compared to similar vehicles. Let’s assume these statistics remain the same for 2017. That is, 2.7 percent of new car sales are hybrids in the first quarter of 2017. For a sample of 40 vehicles sold in the Richmond, Virginia area:

a. How many vehicles would you expect to be hybrid?

b. Use the Poisson distribution to find the probability that five of the sales were hybrid vehicles.

c. Use the binomial distribution to find the probability that five of the sales were hybrid vehicles.

Answer 1

Expected is 2.7% of 40 = 1.08

lamba = 0.027

poisson f(x) = lambda^k * exp(-lambda)/k!

f(5) = 0.027^5 * exp(-0.027)/5! = 0.000000001163889161...

which is essentially zero up to the 10th decimal place (8th as a percent)

binomial

(40 choose 5) * 0.027^5 *0.973^35 = 0.003622... or roughly 0.3622...%