What to Submit:Consider the Toronto area (Toronto Airport). The goal is to work outthe probability of having to award refunds in this area. From these probabilities, you can also calculate the expected cost of the refund per dollar in this area (which will presumably be used by the insurance company to determine the premium which they will charge to cover the refund scheme). First, you need to estimate the distribution of annual snowfall in Toronto using the historical data from 1940 to 1982 (the last column named "total" in the data set). If you plot the histogram of annual snowfall data with StatTools, you will see that the histogram is almost symmetrical. Assume that the annual snowfall in Toronto has a Normal distribution (when we finish hypothesis testing in a few weeks, you can use normality tests to verify that the distribution is normal). Second, use the sample of annual snowfall to estimate the parameters of the Normal distribution. Calculate the sample average and use it as an estimate for the actual mean of annual snowfall. Also, calculate the sample standard deviation and use is as an estimate for the actual standard deviation of annual snowfall.

Note that Firestone uses the average annual snowfall in the last 10 years to award refunds. For the Toronto area, the 10-year average in the advertisement is 130.9 cm. Answer the following questions:

1. What are the estimates for the mean and standard deviation of annual snowfall in Toronto based on the sample of annual snowfall in the area from 1940 to 1982?
2. Calculate the expected cost of refund per dollar in Toronto in the coming year using the estimates for the mean and standard deviation of annual snowfall.
3. How would the refund probabilities be affected if the true standard deviation of annual snowfall were higher than the sample standard deviation? What if the true standard deviation were lower?
4. Evaluate (qualitatively) the value of the refund program to the consumer buying a snow tire in Toronto and to Firestone. Who is the major winner?