18. Forecasting Earnings A researcher notes that senior corporation executives are not very accurate forecasters of their own annual earnings. He states that his studies of a large number of company executive forecasts “showed that the average estimate missed the mark by 15%.”

a. Suppose the distribution of these forecast errors has a mean of 15% and a standard deviation of 10%.

Is it likely that the distribution of forecast errors is approximately normal?

b. Suppose the probability is .5 that a corporate executive’s forecast error exceeds 15%. If you were to sample the forecasts of 100 corporate executives, what is the probability that more than 60 would be in error by more than 15%?