Question

11. (6 pts) The Mountain States Office of State Farm Insurance Company reports that approximately 85% of all automobile damage liability claims were made by people under 25 years of age. A random sample of eight automobile insurance claims is under study.

               

a) Find and interpret the expected number of claims that are made by people under 25 years of age.

b) Find the standard deviation for the number of claims that are made by people under 25 years of age.

c) An insurance agent examines a random sample of 8 claims. Use the mean and standard deviation to determine if it is unusual for all of the claims to be made by people under 25 years of age. Show your work.

Answer 1

given data are sample n =8

p=85% all automobile damage liability claims were made by people under 25 years of age.=0.85

then q=1-p= 1-0.85= 0.15

a) expected number = np

=8×0.85 =6.8

b) standard deviation =

=

=1.01

c) The unusual values for all of the claims to be made by people under 25 years of age are

and

those are

x1=

= 6.8- 2×1.01

=6.8- 2.02 = 4.78

x2=

=6.8+2×1.01

=6.8+2.02 =8.82