According to the Earth Policy Institute (July 2013), 60% of the world's solar energy cells are manufactured in China. Consider a random sample of 5 solar energy cells, and let x represent the number in the sample that are manufactured in China. In Section 4.4, we show that the probability distribution for x is given by the formula

where n! = (n) (n - 1) (n - 2) ........ (2) (1)
a. Explain why x is a discrete random variable.
b. Find p(x) for x = 0, 1, 2, 3, 4, and 5.
c. Show that the properties for a discrete probability distribution are satisfied.
d. Find the probability that at least 4 of the 5 solar energy cells in the sample are manufactured in China?