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Chapter 7: Q. 20 (page 464)

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,\(10)or the statement, “This ticket is not a winner.” Monetary prizes can be redeemed for groceries at the store. Here are the distribution of the prize values and the associated probabilities for each prize:

Which of the following are the mean and standard deviation, respectively, of the winnings?
\)15.00,\(2900.00
(b) \)15.00,\(53.85
(c) \)15.00,\(26.9

(d) \)156.25,\(53.85

(e) \)156.25,$26.93

Short Answer

Expert verified

The mean and standard deviation are $15and $53.83. So, the correct answer is option(b).

Step by step solution

01

Given information

A grocery chain runs a prize game by giving tickets. Printed on the ticket is a dollar value ($500,$100,$10). To determine the mean and standard deviation of the winnings.

02

Explanation

The mean is determined by:

Mean=∑x×P(x)=500(0.01)+100(0.05)+25(0.20)+0(0.74)=15
The standard deviation is calculated by:
σ=∑x2×P(x)-∑x×P(x)2=5002×0.01+1002×0.05+….+02×0.74-(15)2=2900=53.83
Hence, the mean and standard deviation are $15and $53.83.

So, option (b) is correct answer.

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Most popular questions from this chapter

A 10-question multiple-choice exam offers 5choices for each question. Jason just guesses the answers, so he has a probability 1/5of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. One correct way to use a table of random digits to do this is the following:

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(e) Two digits from the random digit table simulate one answer, with 00to 05=right and 06to 99= wrong. Ten pairs of digits from the table simulate 10answers.

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