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Chapter 7: Q. 2.20 (page 491)

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) The mean and standard deviation, respectively, of the winnings are$15.00,$53.85.

Step by step solution

01

Given information

Given,

Amount won
$500
$100
$100$0
Probability0.01

0.05		0.20
0.74

Below is the formulae used to get the result,

渭=鈭�x脳p(x)蟽2=鈭�(x-渭)2脳p(x)蟽=蟽2
02

Explanation for correct option

Let's consider,

渭=500脳0.01+100脳0.05+25脳0.20+0脳0.74=15

Variance

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

The standard deviation (SD)

蟽=2900=53.85

Therefore, the correct option is (b)

03

Explanation for incorrect option

(a) The mean and standard deviation, respectively, of the winnings will not be$15.00,$2900.00.

(c)The mean and standard deviation, respectively, of the winnings will not be$15.00,$26.93.

(d)The mean and standard deviation, respectively, of the winnings will not be$156.25,$53.85.

(e)The mean and standard deviation, respectively, of the winnings will not be$156.25,$26.93.

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