29. Suppose that U1,U2, . . . is a sequence of independent uniform (0,1) random variables, and define N by N = min{n : U1 +· · ·+Un > 1}

That is, N is the number of uniform (0, 1) random variables that need be summed to exceed 1. Use random numbers to determine the value of 36 random variables having the same distribution as N, then use these data to obtain a 95 percent confidence interval estimate of E[N]. Based on this interval, guess the exact value of E[N].