Problem 6. (15 + 5 exta credit points : Assume that X is Normally wastribute.. The population ma-is YU, = a a SD,X, = w. Suppos. that in practice. u and o fr) .of known, so > is sampleu. Let Xve the sample mean of n mutually independent samples XX. . . . . X. ay As a function of u n and or o, what is the formula for EX]. w/ As a function of u, n, and or o, what is the formula for SD, X . c) What type of distribution does X follow? d) (.=tra credit opportunity - 5 points possible) Suppose that an anal, st named Fred does not know u or o, but in one trial of an experiment is able to sample X a total of n = 25 times. Fred's null hypothesis is H. : us 100. The level of significance is a = .05 . Create a simulation of this experiment: Suppose that you actually know that u = 30 and o = 20 (but Fred does not know this,. For each trial, determine Fred's test statistic, and indicate (in Excel, whether or not there is a Type I error. Simulate (only) 100 trials of the experiment and report (in Excel, the fraction of the 100 trials in which there is a Type I error