1. Let us assume that the life of a tire (in miles), say X , is normally distributed with mean ,u, and standard deviation 0 known to be 5,000 miles. Past experience indicates that ,u = 30, 000. The manufacturer claims that the tires made by a new process have mean u > 30,000 and it is very possible that ,u = 35, 000. Let us check their claim by testing Ho : p S 30, 000 versus H1 : ,u. > 30, 000. We shall observe a_large number n independent values of X say X1, X2, . . . ,Xn and we shall reject the null hypothesis if X 2 k. Determine n and It so that the signicance level a = 0.01 and the type II error rate at ,u = 35, 000 is no more than 1.79%