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Question

1. The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10k race (a 10k race with obstacles). Which of the following is closest to the mean of the following data set?

1.0, 1.1, 1.2, 1.2, 1.3, 1.4, 1.4, 1.4, 1.5

a. *x *is about 1.1 hours

b. *x *is about 1.3 hours

c. *x *is about 1.5 hours

d. *x *is about 1.6 hours

2. Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men. Chose the statement that best summarizes the meaning of the standard deviation.

Women: *s *= 0.17 Men: *s*= 0.21

a. On average, men’s finish times will be 0.21 hours faster than the overall average finish time.

b. On average, women’s finish times will be 0.17 hours less than men’s finish times.

c. The distribution of men’s finish times is less varied then the distribution of women’s finish times.

d. The distribution of women’s finish times is less varied then the distribution of men’s finish times.

3. A city planner says, “The typical commute to work for someone living in the city limits is less than the commute to work for someone living in the suburbs.” What does this statement mean?

a. If you live in the city limits you will have a longer commute time.

b. The center of the distribution of commute times for a city-dweller is less than the center of the distribution for those living in the suburbs.

c. All city dwellers spend less time commuting to work than those living in the suburbs.

d. There is less variation in the commute time of those living in the suburbs.

The following list shows the age at appointment of U. S. Supreme Court Chief Justices appointed since 1900. Use the data to answer questions (4), (5), and (6).

4. Find the mean, rounding to the nearest tenth of a year, and interpret the mean in this context.

a. The typical age of a U. S. Supreme Court Chief Justice appointed since 1900 is 63.0.

b. The typical age of a U. S. Supreme Court Chief Justice appointed since 1900 is 64.1.

c. The typical age of a U. S. Supreme Court Chief Justice appointed since 1900 is 61.4.

d. The typical age of a U. S. Supreme Court Chief Justice appointed since 1900 is 61.0.

5. The U. S. Supreme Court Chief Justice data was used to create the following output in an Excel spreadsheet. Choose the statement that best summarizes the variability of the dataset.

a. The age of most of the U. S. Supreme Court Chief Justice’s since 1900 are within 5.6 years of the mean age.

b. The age of most of the U. S. Supreme Court Chief Justice’s since 1900 are within 31.3 years of the mean age.

c. The ages of most of the U. S. Supreme Court Chief Justices are between 50 and 68 years. d. None of the above.

Use the following information to answer questions (6)-(9). The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses’ ages is approximately unimodal and symmetric.

6. Between what two values would you expect to find about 95% of the lead actresses ages?

a. 23.25 and 35.95 years

b. 10.55 and 48.65 years

c. 16.9 and 42.3 years

d. None of the above

7. Between what two values would you expect to find about 68% of the lead actresses ages?

a. 23.25 and 35.95 years

b. 10.55 and 48.65 years

c. 16.9 and 42.3 years

d. None of the above

8. In 2010, actress Helena Bonham Carter was in the movie “The King’s Speech.” She was 44. Was it unusual for a 44-year old actress to be in a top grossing film of 2010? Assume the Empirical Rule holds and find the z-score and whether it was unusual.

a. * _{z }*=

_{2.27 }Most people would say it is unusual.

b. * _{z}*=−

_{2.27}Most people would say it is not unusual.

c. * _{z }*=

_{0.27 }Most people would say it is unusual.

d. * _{z}*=−

_{0.27}Most people would say it is not unusual.

9. In 1993, actress Anna Paquin won an academy award in for the movie “The Piano”. She was 11-years-old. Finish the statement: “According to the Empirical Rule, the ages of nearly all lead actresses will be between ______ and _____ years. Anna Paquin was ___________ this range when she won the academy award.”

a. 16.9; 42.3; not within

b. 10.6; 48.7; within

c. 10.6; 48.7; not within

d. 23.3; 36.0; within

10. The mean price of a pound of ground beef in 75 cities in the Midwest is $2.11 and the standard deviation is $0.56. A histogram of the data shows that the distribution is symmetrical. A local Midwest grocer is selling a pound of ground beef for $3.25. What is this price in standard units? Assuming the Empirical Rule applies, would this price be unusual or not? Round to the nearest hundredth.

a. * _{z }*=

_{2.04 }; This is unusually expensive ground beef.

b. * _{z }*=

_{2.04 }; This price would not be unusual.

c. * _{z }*=−

_{2.04 }; This price would not be unusual.

d. * _{z }*=−

_{2.04 }; This is unusually inexpensive ground beef.