A large corporation in search of a CEO and a CFO has narrowed the fields for each position to a short list. The CEO candidates graduated from Chicago (C) and three Ivy League universities: Harvard (H), Princeton (P), and Yale (Y). The four CFO candidates graduated from MIT (M), Northwestern (N), and two Ivy League universities: Dartmouth (D) and Brown (B). The personnel director wishes to determine the distribution of the number of Ivy League graduates who could fill these positions.

a. Assume the selections were made randomly.

Construct the probability distribution of the number of Ivy League graduates who could fill these positions.

b. Would it be surprising if both positions were filled with Ivy League graduates?

c. Calculate the expected value and standard deviation of the number of Ivy League graduates who could fill these positions.