Mean or Expected Value and Standard Deviation · Exercise 28

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

$$\begin{array}{cc}\text{x}& \text{P(x)}\\ \text{0}& \text{0.03}\\ \text{1}& \text{0.50}\\ \text{2}& \text{0.24}\\ \text{3}& \\ \text{4}& \text{0.07}\\ \text{5}& \text{0.04}\end{array}$$

(a) Describe the random variable X in words.
(b) Find the probability that a customer rents three video games.
(c) Find the probability that a customer rents at least four video games.
(d) Find the probability that a customer rents at most two video games.
Another shop, Games Galore, also rents video games. The probability distribution for video game rentals per customer at this shop is given as follows. Games Galore also has a five-game limit per customer.
$$\begin{array}{cc}\text{x}& \text{P(x)}\\ \text{0}& \text{0.35}\\ \text{1}& \text{0.25}\\ \text{2}& \text{0.20}\\ \text{3}& \text{0.10}\\ \text{4}& \text{0.05}\\ \text{5}& \text{0.05}\end{array}$$
(e) At which store is the expected number of video games rented per customer higher?
(f) If Game Stop estimates that they will have 300 customers next week, how many video games do they expect to rent next week? Answer in sentence form.
(g) If Game Stop expects 300 customers next week, and Games Galore projects that they will have 420 customers, for which store is the expected number of video game rentals for next week higher? Explain.
(h) Which of the two stores experiences more variation in the number of video game per customer? How do you know that?

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

OpenStax, Introductory Statistics 2e · §4.2 Mean or Expected Value and Standard Deviation · Exercise 28