Let X be the average of a sample of size 25 independent normal random variables with mean

Question

0 and variance 1. P[[X<c]=0.5
(a) Determine c such that
(b) Now assume that the observations may not be normally distributed, but they still are
independent with mean 0 and variance 1. Find an upper bound on the probability that P[[X<c]
with c taken from the first part of the question.