Mean or Expected Value and Standard Deviation · Exercise 28

People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video to Go is given in the following table. There is a five-video limit per customer at this store, so nobody ever rents more than five DVDs.

$$\begin{array}{cc}\text{x}& \text{P(x)}\\ \text{0}& \text{.03}\\ \text{1}& \text{.50}\\ \text{2}& \text{.24}\\ \text{3}& \\ \text{4}& \text{.07}\\ \text{5}& \text{.04}\end{array}$$

(a) Describe the random variable X in words.
(b) Find the probability that a customer rents three DVDs.
(c) Find the probability that a customer rents at least four DVDs.
(d) Find the probability that a customer rents at most two DVDs.
Another shop, Entertainment Headquarters, rents DVDs and video games. The probability distribution for DVD rentals per customer at this shop is given as follows. They also have a five-DVD limit per customer.
$$\begin{array}{cc}\text{x}& \text{P(x)}\\ \text{0}& \text{.35}\\ \text{1}& \text{.25}\\ \text{2}& \text{.20}\\ \text{3}& \text{.10}\\ \text{4}& \text{.05}\\ \text{5}& \text{.05}\end{array}$$
(e) At which store is the expected number of DVDs rented per customer higher?
(f) If Video to Go estimates that they will have 300 customers next week, how many DVDs do they expect to rent next week? Answer in sentence form.
(g) If Video to Go expects 300 customers next week, and Entertainment Headquarters projects that they will have 420 customers, for which store is the expected number of DVD rentals for next week higher? Explain.
(h) Which of the two video stores experiences more variation in the number of DVD rentals per customer? How do you know that?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §4.2 Mean or Expected Value and Standard Deviation · Exercise 28