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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:

渭=鈭�x脳p(x)蟽2=鈭�(x-渭)2脳p(x)蟽=蟽2

02

Explanation for correct option

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

Standard deviation

蟽=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

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is and the standard deviation of the loss is 蟽=\(5000.The distribution of losses is strongly right-skewed: many policies have \)0loss, but a few have large losses. The company hopes to sell 1000 of these policies for \(300each.

a. Assuming that the company鈥檚 claim is true, what is the probability that the mean loss from fire is greater than \)300for an SRS of 1000 homeowners?

b. If the company wants to be 90% certain that the mean loss from fire in an SRS of 1000 homeowners is less than the amount it charges for the policy, how much should the company charge?

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

a. (10065)(0.71)65(0.29)3510065(0.71)65(0.29)35

b. (10065)(0.29)65(0.71)3510065(0.29)65(0.71)35

c.

P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

d.P(z鈮�0.65-0.71(0.65)(0.35)100)Pz鈮�0.65-0.71(0.65)(0.35)100

e.P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

The mean of this distribution (don鈥檛 try to find it) will be

a. very close to the median.

b. greater than the median.

c. less than the median.

d. You can鈥檛 say, because the distribution isn鈥檛 symmetric.

e. You can鈥檛 say, because the distribution isn鈥檛 Normal.

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72%said they had voted in the election. Election records show that only 56%of registered voters voted in the election. Which of the following statements is true?

a. 72%is a sample; 56%is a population.

b. 72%and 56%are both statistics.

c. 72%is a statistic and 56%is a parameter.

d. 72%is a parameter and 56%is a statistic.

e. 72%and 56%are both parameters.

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
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