CHAPTER 5



Normal Distributions Name Per

Suppose that the BAC of male students at a particular college who drink 5 beers varies from student to student according to a normal distribution with mean 0.08 and standard deviation 0.01. The next three questions use this information.

1. The middle 95% of students who drink 5 beers have BAC between

(a) 0.07 and 0.09 (b) 0.06 and 0.10 (c) 0.05 and 0.11 (d) 0.04 and 0.12

2. What percent of students who drink 5 beers have BAC above 0.08 (the legal limit for driving in most states)?

(a) 2.5% (b) 5% (c) 16% (d) 32% (e) 50%

3. What percent of students who drink 5 beers have BAC above 0.09 (the legal limit for driving other states)?

(a) 2.5% (b) 5% (c) 16% (d) 32% (e) 50%

4. SAT scores are normally distributed with mean 500 and standard deviation 100. Julie scores 650. Her standard score is

(a) 150 (b) 15 (c) 1.5 (d) 0.15

5. For a normal distribution with mean 20 and standard deviation 5, approximately what percent of the observations will be less than 20?

(a) 50% (b) 68% (c) 95% (d) 99.7% (e) 100%

6. For a normal distribution with mean 20 and standard deviation 5, approximately what percent of the observations will be less than 10?

(a) 99.7% (b) 97.5% (c) 2.5% (d) 95% (e) 99%

7. You are told that your score on an exam is at the 85 percentile of the distribution of scores. This means that

(a) You score was equal to or lower than approximately 85% of the people who took this exam

(b) You score was equal to or higher than approximately 85% of the people who took this exam

(c) You answered 85% of the questions correctly

(d) The correlation between your score and the exam is 0.85.

(e) You are 85% confident in your score is significant

8. If you know the mean and standard deviation of a distribution, do you know the complete shape of the distribution?

(a) Yes, always.

(b) Yes if the distribution is normal, but not in general.

(c) Yes if the distribution is symmetric, but not in general.

(d) No, never.

9. The distribution of heights of adult men is approximately normal with mean 69 inches and standard deviation 2.5 inches. About what percent of men are taller than 74 inches?

(a) 95% (b) 68% (c) 16% (d) 5% (e) 2.5%

10. The distribution of heights of adult men is approximately normal with mean 69 inches and standard deviation 2.5 inches. How tall is a man whose standardized height is -0.3?

(a) 68.25 inches (b) 68.7 inches (c) 69.3 inches (d) 69.75 inches

11. Wayne's buddy Garth took the SAT. His standard score on the SAT was 0.3. This means that Garth's actual score was

(a) more than 1 standard deviation below the mean SAT score.

(b) less than 1 standard deviation below the mean SAT score.

(c) less than 1 standard deviation above the mean SAT score.

(d) more than 1 standard deviation above the mean SAT score.

12. If the heights of 99.7% of American men are between 5'0" and 7'0", what is your estimate of the standard deviation of the height of American men?

(a) 1 inch (b) 3 inches (c) 4 inches (d) 6 inches (e) 12 inches

13. The mean is 80 and the standard deviation is 10. What is the standard score for an observation of 90?

(a) 90 (b) 0 (c) 10 (d) 1.0 (e) -1.0

The next three questions are based on the following information: Scores on the 1992 SAT verbal exam were normally distributed, with mean 480 and standard deviation about 100.

14. The median score was

(a) 100 (b) 480 (c) 680 (d) can't be determined

15. What percent of all students scored below 400?

(a) -0.8% (b) 0.8% (c) 21.19% (d) 78.81%

16. What percent of all students scored above 600?

(a) 1.2% (b) 11.51% (c) 13.5% (d) 88.49%

17. About what score would a student have to get to be in the 99th percentile?

(a) 679 (b) 699 (c) 710 (d) 750

The next two questions concern the normal curve below.

[pic]

18. The mean of this normal distribution is

(a) about 10 (b) about 50 (c) about 60 (d) about 70

19. The standard deviation of the normal distribution is

(a) about 5 (b) about 10 (c) about 20 (d) about 60

Univariate Data

20. You have similar data on returns on common stocks for all years since 1945. To show clearly how returns have changed over time, your best choice of graph is

(a) a bar graph (b) a line graph (c) a pie chart

(d) a histogram (e) a scatterplot

The stock market did well during the 1990s. Here are the percent total returns (change in price plus dividends paid) for the Standard & Poor's 500 stock index:

[pic]The next five questions are related to this situation.

21. The median return during this period is

(a) 5.5 (b) 20.07 (c) 23.0 (d) 25.8 (e) 28.6

22. The third quartile of these returns is

(a) 7.6 (b) 30.5 (c) 31.1 (d) 31.7 (e) 33.4

23. The mean return is

(a) 20.07 (b) 20.69 (c) 22.3 (d) 25.8 (e) 33.4

24. The standard deviation of the returns is

(a) 13.75 (b) 13.98 (c) 14.74 (d) 20.07 (e) 25.8

25. According to the student newspaper, the mean salary of male full professors in the School of Management is $117,302. The median of these salaries

(a) would be lower, because salary distributions are skewed to the left.

(b) would be lower, because salary distributions are skewed to the right.

(c) would be higher, because salary distributions are skewed to the left.

(d) would be higher, because salary distributions are skewed to the right.

26. A well-drawn histogram should have

(a) bars all the same width

(b) no space between bars (unless a class has no observations)

(c) a clearly marked vertical scale

(d) all of these

27. To illustrate a talk you are giving, you want to make a graph to compare the percents of adults in several countries who have finished university. For example, this percent is 9% in France and 24% in the United States. You should make a

(a) bar graph

(b) histogram

(c) line graph

(d) pie chart

28. Jorge's score on Exam 1 in his statistics class was at the 64th percentile of the scores for all students. His score falls

(a) between the minimum and the first quartile

(b) between the first quartile and the median

(c) between the median and the third quartile

(d) between the third quartile and the maximum

29. The percents of students in the five classifications should add to 100%. In fact, they add to only 99.9%. The reason is that

(a) There must be an arithmetic mistake.

(b) The percents are not exact, because they are rounded to one decimal place.

(c) Some students must be left out, so the total should be less than 100%.

(d) This is an example of a biased measurement.

Here are boxplots of the number of calories in 20 brands of beef hot dogs, 17 brands of meat

hot dogs, and 17 brands of poultry hot dogs.

[pic]

30. This plot shows that

(a) all poultry hot dogs have fewer calories than the median for beef and meat hot dogs

(b) about half of poultry hot dog brands have fewer calories than the median for beef and meat hot dogs

(c) hot dog type is not helpful in predicting calories, because some hot dogs of each type are high and some of each type are low

(d) most poultry hot dog brands have fewer calories than most beef and meat hot dogs, but a few poultry hot dogs have more calories than the median beef and meat hot dog

31. We see from the plot that the median number of calories in a beef hot dog is about

(a) 190 (b) 179 (c) 153 (d) 139 (e) 129

32. The calorie counts for the 17 poultry brands are:

129 132 102 106 94 102 87 99 170 113 135 142 86 143 152 146 144

The median of these values is

(a) 129 (b) 132 (c) 130.5 (d) 121 (e) 170

33. The first quartile of the 17 poultry hot dog calorie counts is

(a) 99 (b) 102 (c) 100.5 (d) 143.5 (e) 143

34. Which of these is not true of the standard deviation s of the lengths in inches of a sample of brook trout?

(a) s must take a value between -1 and 1.

(b) s is measured in inches.

(c) s would not change if we measured these trout in centimeters instead of inches.

(d) Both (b) and (c).

(e) Both (a) and (c).

35. For a distribution that is skewed to the right, usually

(a) the mean will be larger than the median

(b) the median will be larger than the mean

(c) the first quartile will be larger than the third quartile

(d) the standard deviation will be negative

(e) the minimum will be larger than the maximum

36. When dealing with financial data (such as salaries or lawsuit settlements), we often find that the shape of the distribution is ________ . When the distribution has this shape, the ________ is pulled toward the long tail of the distribution, but the ________ is less affected. The sequence of words to correctly complete this statement is:

(a) right skewed, median, mean.

(b) left skewed, mean, median.

(c) right skewed, mean, standard deviation.

(d) right skewed, mean, median.

(e) roughly symmetric, mean, correlation.

Bivariate Data

37. The correlation of U.S. stock returns with overseas stock returns during these years was

r = 0.44. This tells you that

(a) when U.S. stocks rose, overseas stocks also tended to rise, but the connection was not very strong

(b) when U.S. stocks rose, overseas stocks rose by almost exactly the same amount

(c) when U.S. stocks rose, overseas stocks tended to fall, but the connection was not very strong

(d) there is almost no relationship between changes in U.S. stocks and changes in overseas stocks

(e) nothing, because this is not a possible value of r

38. If x is the return on U.S. stocks and y is the return on overseas stocks in the same year, the least-squares regression line for predicting y from x is y = -2.7 + 0.47x. You think U.S. stocks will have a return of 10% in 1999. Using this regression line, you predict that the return on overseas stocks will be

(a) 7.4% (b) -2.23% (c) 2% (d) 3.17%

39. Which statistical measure is not strongly affected by a few outliers in the data?

(a) the mean

(b) the median

(c) the standard deviation

(d) the correlation coefficient

40. The correlation between two variables is of -0.8. We can conclude

(a) one causes the other

(b) there is a strong positive association between the two variables

(c) there is a strong negative association between the two variables

(d) all of the relationship between the two variables can be explained by a straight line

(e) there are no outliers

41. If the least squares regression line for predicting y from x is y = 500 - 20x, what is the predicted value of y when x = 10?

(a) 300 (b) 500 (c) 200 (d) 700 (e) 20

42. The equation of the regression line for son's height in inches y versus father's height in inches x is y = 0.5x + 35. For 72 inch tall fathers, what is the mean height of their sons?

(a) 69 inches (b) 71 inches (c) 72 inches (d) 74 inches

(e) None of the above.

How well does the number of beers a student drinks predict his or her blood alcohol content? Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). A scatterplot of the data appears below.

[pic]

43. The scatterplot shows

(a) a weak negative relationship

(b) a moderately strong negative relationship

(c) almost no relationship

(d) a weak positive relationship

(e) a moderately strong positive straight-line relationship between number of beers and BAC.

44. A plausible value of the correlation between number of beers and blood alcohol content, based on the scatterplot, is

(a) r = -0.8 (b) r = -0.3 (c) r close to 0 (d) r = 0.3 (e) r = 0.8

45. The least-squares regression line for predicting blood alcohol content from number of beers is y = -0.013 + 0.018x. The slope 0.018 of this line tells us that

(a) the correlation between number of beers and BAC is 0.018

(b) on the average, BAC increases by 0.018 for each additional beer a student drinks

(c) a student who drinks no beer will still have a BAC of 0.018

(d) the average BAC of all the students in the study was 0.018

46. The least-squares regression line for predicting blood alcohol content from number of beers is y = -0.013 + 0.018x. Using this line, you predict that the BAC of a student who drinks 5 beers will be about

(a) 0.025 (b) 0.077 (c) 0.09 (d) 0.103

47. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

(a) much smaller that 0.52

(b) slightly smaller than 0.52

(c) unchanged: equal to 0.52

(d) slightly larger than 0.52

(e) much larger that 0.52

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