In the following probability distribution, the random variable X represents the number of activities a parent of a student in kindergarten through fifth grade is involved in.

X 0 1 2 3 4
P(X) 0.035 0.074 0.197 0.320 0.374

a) Verify that this is a valid discrete probability distribution.

b) What is the probability that a randomly selected student has a parent involved in three activities?

c) Is it unusual for a parent of a randomly selected student to not be involved in any activities? Explain why or why not.

d) Compute the mean of the random variable X.

e) Compute the standard variation of the random variable X.