Question

The Mountain States Office of State Farm Insurance Company reports that approximately 73% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.

(a) Make a histogram showing the probability that r = 0 to 12 claims are made by people under 25 years of age.

(b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)

μ =

σ =

For samples of size 12, what is the expected number of claims made by people under 25 years of age? (Round your answer to the nearest whole number.)

Answer 1

This will be a Binomial distribution with parameters:

n = 12, p = 0.73

Hence,

a) Since the probability is greater than 0.5, this distribution will be left skewed. Hence,

Graph B is correct.

b) Mean = np = 12*0.73 = 8.76

Standard deviation = = 1.54

pq = V12 * 0.73 * 0.27

Expected number of claims made = 9