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Chapter 7: Q.AP2.20 - Cumulative AP Practise Test (page 438)

AP2.20 A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ( \( 500, \) 100, \(25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket:

Which of the following are the mean and standard deviation, respectively, of the winnings?

a. \) 15.00, \( 2900.00

b.\) 15.00, \( 53.85

c. \) 15.00, \( 26.93

d. \) 156.25,\( 53.85

e. \) 156.25, $ 26.93

Short Answer

Expert verified

b.$ 15.00, $ 53.85

Step by step solution

01

Given Information

Formula used:

μ=∑x×p(x)σ2=∑(x-μ)2×p(x)σ=σ2

02

Explanation for correct option

μ=500×0.01+100×0.05+25×0.20+0×0.74=15

Variance

σ2=(500-15)2×0.01+(100-15)2×0.05+(25-15)2×0.20+(0-15)2×0.74=2900

Standard deviation

σ=2900=53.85

Hence, the correct option is (b)

03

Explanation for incorrect option

a. $ 15.00, $ 2900.00 is not the answer.

c. $ 15.00, $ 26.93 is not the answer.

d. $ 156.25,$ 53.85 is not the answer.

e. $ 156.25, $ 26.93 is not the answer.

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Most popular questions from this chapter

Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 3%of such operations, the repair fails in 14%, and both infection and failure occur together 1%of the time. What is the probability that the operation is successful for someone who has an operation that is free from infection?

a. 0.8342

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