Consider a sequence of independent random variables Xi, each with a standard normal distribution.
(a) What is P(|Xi| ≤ 0.5)?
(b) If  is the average of eight of these random variables, what is P(|| ≤ 0.5)?
(c) In general, if  is the average of n of these random variables, what is the smallest value of n for which P(|| ≤ 0.5) ≥ 0.99?