Question

Let x1,x2,x3 be random sample of normal(6,4), find P(max{x1,x2,x3}>8)

Answer 1

Look up normal probability table for X~N(6,4) for P(X<8)=0.69 (approx.), so

P(X>8)=0.31.

Since we have random samples which we assume to be independent, we can use binomial probability distribution to calculate P(max{x1,x2,x3}>8).
Alternatively, we can calculate
P(all X<8)=0.69&sup3, then
P(at least one >8)=1-0.69³.