Question

The population of scores on the SAT forms a normal distribution with μ =500 and σ = 100. If you take a random sample of n =100 what is the probability that the sample mean will be greater than M = 520

Answer 1

P(M > 520) = 1 - P(M < 520) = 1 - P(z < (520 - 500)/(100/sqrt(100))) = 1 - P(z < (20/(100/10))) = 1 - P(z < 20/10) = 1 - P(z < 2) = 1 - 0.97725 = 0.02275