An insurance company has a portfolio of 10,000 policies. Based on past data the company

estimates that the probability of a claim on any one policy in a year is 0.003. It assumes

no policy will generate more than one claim in a year.

(a) Determine the approximate probability of more than 40 claims from the portfolio

of 10,000 policies in a year.

(b) Determine an approximate equal-tailed interval into which the number of claims

per year will fall with probability 0.95.

(c) In practice 42 claims were received in a particular year. A Director of the company

complains about the range of estimates in part (b) being wrong.

Comment on the Director's complaint.

An industry survey of people in sales management positions gave the number of years

of experience in sales related positions as shown below.

Males Females

Sample size 90 80

Mean years 25:7 22:5

Standard deviation years 8:2 3:5

(a) Construct a 95% confidence interval for the difference of population means.

(b) Perform a test to determine if the mean number of years for males in sales related

positions is more than one year larger than that of females?