PROBABILITY (with solutions)

4.The lengths of trout in a certain lake are normally distributed with a mean of 7' inches and a standard deviation of 2 inches. If the fish and game department would like shermen to keep only the largest 20% of the trout, what should the minimum size for "keepers\" be? 5. The following figures refer to the times (in minutes) that eight customers spent from the time they entered a store to the time they left: 6, 3, 2, 10, 2, 5, 4, 6. Find (a) the arithmetic mean and {b) the mean deviation. 6. An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault on rare occasions causes a catastrophe at high speed. Assume that the distribution of the number of cars per year will experience the fault is 3 on the average, find the probability that (a) at most 3 cars per year will experience a catastrophe, (b) more than 1 car per year will experience a catastrophe