Insurance Companies track life expectancy information to assist in determing the cost of life insurance policies

Insurance Companies track life expectancy information to assist in determing the cost of life insurance policies. Last year the average life expectancy of all policy holders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The ages of the clients in the sample are shown below.

86 75 83 84 81 77 78 79 79 81

76 85 70 76 79 81 73 74 72 83

a) Based on the sample results, find the 90% cofidence interval and interpret

b) For more accurate cost determination, ABI Insurance wants to estimate the average life expectancy to within one year with 95% cofidence. How many randomly selected recently paid policies would they need to sample?

c) Suppose ABI samples 100 recently paid policies. This sample yields a mean of 77.7 years and a standard deviation of 3.6 years. Find a 90% cofidence interval and interpret.