For problem 2 I would like to confirm my answer for A and ask a question about C.

2.) according to admission statistics, the whole stern MBA class has an average GMAT score of 721. Assume that a randomly chosen student GMAT score follows a normal distribution, with mean 721 and standard deviation 31.3.

a. What is the probability of a randomly chosen students GMAT score being greater than 730? answered below- please review

c. What is the probability that the average GMAT score of the five members of a randomly selected study group is less than 680? Please advise how to go about this.

mu = 721

st dev = 31.3

P(> 730)

=P((x - 730) / 31.3) > ((721 - 730) / 31.3)

= P(Z > -0.28753994)

When looking at the Standard Normal CDF Table (Negative Values), I looked for -0.2 and 0.08 -> = 0.3897

This 0.3897 represents the area under the curve and to the left of the -0.28 value, so in order to obtain P(Z > -0.28) we have to subtract the above value from 1.

1 - 0.3897 = 0.6103

P(X > 730) = 0.6103