Question: 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

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?

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