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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 Table4.37.There is five-video limit per customer at this store, so nobody ever rents more than five DVDs.

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.

Short Answer

Expert verified

a. "x"is the number of DVDs a customer rents

b. Probability that a customer rents three DVDs are 0.11

c. Probability that a customer rents at least four DVDs are 0.09

d. Probability that a customer rents at most two DVDs are0.80

Step by step solution

01

Given information

The probability distribution for DVD rentals per customer at Video To Go is given Table4.37

02

Part (a) Step 1: Explanation

Describe the random variable Xin words.

  1. Xis the number of DVDs a customer owns
  2. X is the total number of DVDs rented at the store
  3. X is the number of DVDs a customer rents
  4. X is the number of customers that come into the store
  5. X is the number of times a single customer comes into the store
03

Part (b) Step 1: Explanation

Since the probability is100%that a person who comes in the store will rent either 0,1,2,3,4,or5DVDs, then we just subtract the others from 100%to get the probability they will rent 3DVDs.

So100%-4%-52%-24%-6%-3%=11%. Therefore, the probability that a person who comes in the store will rent three DVDs is 11%or0.11.

04

Part (c) Step 1: Explanation

The probability that a customer rents at least four DVDs is equal to the probability they will rent 4OR5 DVDs so 6%+3%=9%or0.09.

05

Part (d) Step 1: Explanation

The probability that a customer rents at most two DVDs is equal to te probability they will rent zero OR one, OR two DVDs so4%+52%+24%=80%or0.80.

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