Chapter P, Concept Check Question 2.2a

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P.2.2a

Consider three students with the following distributions of 24 quiz scores:

Amanda:8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

8,8,8,8,8,8

Barney: 5,6,6,6,6,7,7,7,7,7,7,7,8,8, 8,8, 8,8,

8,9,9,9,9,10

Charlene: 0,0,0,0,0,0,0,0,0,0,0,0,10,10,10,10,

10,10,10,10,10,10,10,10

Without bothering to do any calculations, which student has thesmalleststandard deviation of quiz scores?

a. Amanda - more consistency in values

b. Barney - middle range of values

c. Charlene - most extreme range of values

d. You cannot decide without performing the calculations for comparison.

Chapter P.2 Exercise Question 09

P.2.9

The July 8, 2012 edition of the San Luis Obispo Tribune listed predicted high temperatures (in degrees Fahrenheit) for locations throughout San Luis Obispo county (SLO-county) on that date. The newspaper also listed predicted high temperatures for locations throughout California, the United States and around the world. The following dotplots display the four distributions.

Without calculating, arrange the four groups from approximately the highest temperature (on average) to smallest.

a. World, SLO-County, CA, US

b. US, World, SLO-County, CA

c. US, CA, World, SLO-County

d. SLO-County, US, CA, World

Without calculating, arrange the four groups from approximately the most variability in temperatures to least.

a. US, CA, SLO-County, World

b. US, World, SLO-County, CA

c. World, CA, US, SLO-County

d. World, SLO-County, CA, US

Which U.S. city might explain the low outlier in the distribution of the United States temperatures?

a. Juneau, Alaska

b. St. Paul, Minnesota

c. Honolulu, Hawaii

d. Boston, Massachusetts

What might explain the bi-modal shape in the distribution of the world temperatures?

a. Eastern/Western Hemispheres

b. Random chance

c. Northern/Southern Hemispheres

d. Months of the Year

Chapter P.3 Exercise Question 01

P.3.1

It has been reported that the probability that a new business closes or changes owners within its first 3 years is about 0.6. Saying, "About 60% of all new businesses close or change owners within the first three years," would be a correct interpretation of the probability in this case.

a. True

b. False

Chapter P.3 Exercise Question 04

P.3.4

Answer this question for each of the following statements: Which of the following explains what it means to say "the probability of ..." while describing the random process that is repeated over and over again?

The probability of getting a red M&M candy is 0.2.

a. If you repeatedly draw M&Ms at random a very large number of times, in the long-run 20% of those M&Ms will be red.

b. Each time you draw ten M&Ms, two of the M&Ms should be red.

c. For every 100 M&Ms, there should be 20 M&Ms in the bag of candies.

d. All of these are correct interpretations of probability.

The probability of winning at a "daily number" lottery game is 1/1000.

a. If 1000 people play the lottery, exactly one of those playing will win the lottery.

b. Each time the lottery is played, one of 1000 people playing will win.

c. If you repeatedly play the lottery a very large number of times, in the long run, you will win 0.1% of the times you play.

d. All of these are correct interpretations of probability.

The probability of rain tomorrow is 0.3.

a. Thirty percent of the region will receive rain tomorrow.

b. If you repeatedly record whether or not it rains for a large number of days with the same weather conditions as tomorrow, in the long run you will see rain on 30% of such days.

c. Residents of the city should prepare for about 7.2 hours (30% of 24 hours) of rain on the next day.

None of these are correct.

Pennies can be a nuisance. Suppose 30% of the population of adult Americans want to get rid of the penny. If I randomly select one person from this population, the probability this person wants to get rid of the penny is 0.30.

a. If you repeatedly select an adult American at random a large number of times, in the long run, roughly 30% of the time the selected adult will vote b. to get rid of the penny.

c. If you ask 10 people if they are in favor of getting rid of the penny, 3 of them will say yes.

d. There are 30 out of every 100 people who would agree that they would vote to get rid of the penny.

All of these are correct.

Suppose a polling organization takes a random sample of 100 people from the population of adults in a city, (where 30% of this population wants to get rid of the penny). Then the probability is 0.015 that the sample proportion who want to get rid of the penny is less than 0.20.Stating, "If you repeatedly select a sample of 100 adults from this city and record the proportion that want to get rid of the penny for each sample, in the long run roughly 1.5% of these samples will have at most 20% of the sample wanting to get rid of the penny," would explain what it means to say "the probability of ..." while describing the random process that is repeated over and over again.

a. True

b. False

Chapter P.3 Exercise Question 05

P.3.5

Suppose that baseball team A is better than baseball team B. Team A is better by enough that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games.

Explain what it means to say that team A has a 2/3 probability of beating team B in any one game.

If these two games play each other 99 times, team A will win 66 of the 99 games.

a. All answers are equivalent.

b. If these two teams play each other 3 times, team A will win 2 of the three games.

c. If these two teams play each other many, many times under identical conditions, team A will win 2/3 of the games in the long run.

It would be correct to say that if team A plays team B for 3 games, A guaranteed to win exactly twice.

a. True

b. False

It would be correct to say that if team A plays team B for 30 games, A is guaranteed to win exactly twenty games.

a. True

b. False

If team A plays team B for 30 games, is it very likely that team A will win exactly 20 times? Explain.

a. Yes, since the probability has been calculated to be 2/3, we expect team A to win 20 games.

b. Yes, team A will be likely to win twenty of thirty games because the long-run probability is 2/3.

c. This cannot be determined without seeing each game's outcome.

d. No, the proportion of games that team A wins will likely be close to but not exactly 2/3 (such as 18, 19, 20, 21, 22 wins), so there could still be a low probability that A wins exactly 2/3 of the 30 games.