The probability distribution below is for the random variable XXthe number of credits taken by a randomly selected first-year student at a large state university

Credits 14

17

Probability 0.05 0.65

0.10

15

16

0.20

(a) Is X a discrete or a continuous random variable? Explain

(b) Show that the probability distribution of X is valid

(c) Make a histogram of the probability distribution. Describe its shape.

(d) Compute and interpret the expected value of X Show work,

(e) The standard deviation is 0.726. Interpret this value in the context of the problem.

(Express the event taking at least 16 credits in terms of X and find its probability