Question

Consider a sequence of independent random variables, Z_i, i = 1,2,..., each with a standard normal distribution.

Calculate P(|Z_1| < 0.9)

if Z' is the average of 8 of these random variables, what is P(|Z'| < 0.9)?

if Z' is the average of n of these random variables, what is the smallest value of n for which
P(|Z'| < 0.9) >= 0.99?

Answer 1

I'm not completely sure how to begin this one.