1 Let Y be a standard normal random variable Find PY 15 2

1- Let Y be a standard normal random variable. Find P(|Y | > 1.5).

2- Let Z1, Z2, . . . , Z10 be ten independent standard normal random variables. Find the probability that at least six of them are positive.

1. Use excel command ( = 2*(1-NORM.S.DIST(1.5,TRUE))) , answer is 0.133614

2.Atlease six of them are positive means 6,7,8,9,10 can be positive =>

10c6*0.5^10 + 10c7*0.5^10 + ....... 10c10*0.5^10 = 0.5^10 * (10c6+10c7+10c8+10c9+10c10) = 0.5^10 * (210+120+45+10+1) = 0.000977 * 386 = 0.376953