A disciplinary board at a university contains 1 student, 6 faculty, and 1 administrator. A group of 4 board members will be randomly selected to hear a case.

Let the random variable X be the number of faculty selected to hear the case.

a) Find P(X = 3).

Give the probability as a fraction in lowest terms.

P(X = 3) = Blank 1. Fill in the blank, read surrounding text.

b) Find E(X).

Give the final answer as a decimal.

If rounding the final answer, give it to 2 decimal places.

E(X) = Blank 2. Fill in the blank, read surrounding text.

c) Find the standard deviation of the random variable.

Give the final answer as a decimal.

If rounding the final answer, give it to 2 decimal places.

Standard Deviation =