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Chapter 12: Q. AP4.16 (page 829)

Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let X=the number of rolls required to obtain a sum greater than 7. If 100trials are conducted, which of the following is most likely to be the result of the simulation?

a.

b.

c.

d.

e.

Short Answer

Expert verified

The correct answer is option (a).

Step by step solution

01

Given information

X=the number of rolls required to obtain a sum greater than 7.

100 trials are conducted

02

Explanation

Two six-sided dice are tossed, with the sum of the faces shown being recorded after each roll.

Then, any choice other than (a) is invalid, because a sum higher than 7cannot be rolled with 0rolls.

Because the probability of getting a total larger than7 is extremely high, and not doing so on the first try gets increasingly implausible, the majority of trials only require one roll. As a result, option (a) is the proper choice.

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Most popular questions from this chapter

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.4 By about how much does the sample slope typically vary from the population slope in repeated random samples of n=69 golfers?
a. 7,897,179
b. 1,698,371
c. 3,023,782
d. 281,777
e. −4,139,198

In a recent poll, randomly selected New York State residents at various fast-food restaurants were asked if they supported or opposed a "fat tax" on sugared soda. Thirtyone percent said that they were in favor of such a tax and 66% were opposed. But when asked if they would support such a tax if the money raised were used to fund health care given the high incidence of obesity in the United States, 48% said that they were in favor and 49% were opposed.
(a) In this situation, explain how bias may have been introduced based on the way the questions were worded and suggest a way that the questions could have been worded differently in order to avoid this bias.
(b) In this situation, explain how bias may have been introduced based on the way the sample was taken and suggest a way that the sample could have been obtained in order to avoid this bias.
(c) This poll was conducted only in New York State. Suppose the pollsters wanted to ensure that estimates for the proportion of people who would support a tax on sugared soda were available for each state as well as an overall estimate for the nation as a whole. Identify a sampling method that would achieve this goal and briefly describe how the sample would be taken.

If P(A)=0.2and P(B)=0.52 and events A and B are independent, what is P(A or B)?

a. 0.1248

b. 0.28

c. 0.6352

d. 0.76

e. The answer cannot be determined from the given information.

Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains 10identical hummingbird feeders and fills 5, chosen at random, with store-bought food from concentrate and the other 5 with a mixture of sugar and water. The feeders are then randomly assigned to 10possible hanging locations in the researcher’s yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on the amount consumed?

a. A one-sample z-test for a proportion

b. A two-sample z-test for a difference in proportions

c. A chi-square test for independence

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Nicole and Elena wanted to know if listening to music at a louder volume negatively impacts test performance. To investigate, they recruited 30volunteers and randomly assigned 10volunteers to listen to music at 30decibels, 10volunteers to listen to music at 60decibels, and 10volunteers to listen to music at 90decibels. While listening to the music, each student took a 10-question math test. Here is computer output from a least-squares regression analysis using role="math" localid="1654167255833" x=volumeand y=numbercorrect:

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Is there convincing evidence that listening to music at a louder volume hurts test performance? Assume the conditions for inference are met.
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