Question

Insurance companies take risks. When they insure a property or a life, they must price the policy in such a way that their expected profit enables them to survive. They can base their projections on actuarial tables, but the reality of the insurance business often demands that they discount policies to a variety of customers and situations. Managing this risk is made even more difficult by the fact that until the policy expires, the company won

Answer 1

1. The average profit is given by

where x_i's are the profits.

Then, average profit = $1438.902.

2.The standard deviation is given by

Then, the standard deviation = $1329.595.

3. Standard Error is given by

Here, standard error = 242.750.

4.Here . Here population standard deviation is unknown. Then, Margin of Error is given by

Here = 2.045

The the margin of error, E = 496.479.

5. The 95% confidence interval for the mean profit is given by

Hence the 95% confidence interval is (942.420, 1935.380).

6. By 95% confidence we can say that the mean profit made by the sales representative is between $942.420 and $1935.380.