The mean annual salary for male and female graduates of a to

The mean annual salary for male and female graduates of a \"top 20\" MBA program 10 years after graduation is $163,000 and $115,000, respectively. Assume the standard deviation for male graduates is $55,000, and for female gradautes is $30,000. Find the probability that, for a random sample of 200 female graduates, the mean annual salary is at least $115,742.

Solution

let X be the mean salary

Required Probability = P(X > 115742)

= P( Z > (115742 - 115000)/30000/sqrt(200) )

= P(Z > 0.3498 )

From Standard normal table, P(Z > 0.3498) = 0.3632

Therefore, probability that, for a random sample of 200 female graduates, the mean annual salary is at least $115,742 = 0.3632