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and describe the scales of...

1. Describe the following variables as quantitative or qualitative, and describe the scales of measurement.

A. The distance a student commutes from home to campus.

B. The rating of a stock as "strong buy," "buy," "hold," or "sell."

C. The percentage of alcohol (in volume) in Budweiser Beer.

2. A major airline wanted some information on those enrolled in their "frequent flyer" program. A sample of 10 members resulted in the following number of miles flown, to the nearest 1,000 miles, by each participant.

41, 22, 78, 54, 72, 97, 67, 64, 70, 55

A. Use 6 to 14 classes of equal width to create a table of frequencies for the "frequent flyer" data.

B. Draw a stem-and-leaf display for the "frequent flyer" data.

C. Find the first, second, and third quartiles of the "frequent flyer."

3. The following data consists of shoe sizes for six students:

9, 6.5, 8, 8.5, 7.5, 8.5

A. Find the mean shoe size for these six students.

B. Find the standard deviation of the shoe sizes.

4. The following table gives the two-way classification of 2,000 randomly selected employees from a city, based on gender and commuting time from home to work.

Commuting Time from Home to Work:

Less Than 30 Minutes 30 Minutes to One Hour More Than One Hour

Men: 524 455 221

Women: 413 263 124

_____________________________________________________

A. If one employee is selected at random from these 2,000 employees, find the probability that this employee

i. commutes for more than one hour.

ii. commutes for at least half an hour.

iii. commutes for at most one hour given that the employee is a woman.

B. (Are the events "man" and "commutes for more than one hour" independent? Explain.

5. The number of defects in a machine-made product is a random variable with the following probability distribution:

X P(x)

0 0.5

1 0.3

2 0.1

3 0.1

A. Find the probability that there are no more than 2 defects in a product.

B. Find the probability that the number of defects in a product is between 1 and 3, inclusive.

C. Find the probability that a randomly selected product has at most 1 defect.

D. Find the expected number of defects in a product.

E. Find the variance of the number of defects in a product.

6. Twenty percent of the patients treated by a new drug for AIDS show signs of improvement within six weeks. A random sample of five patients is selected and treated by the new drug.

A. Is this a binomial experiment?

B. Find the probability that 4 patients in the sample will show signs of improvement within six weeks.

7. The distance that one professional golfer can drive a golf ball has a normal distribution with a mean of 258 yards and a standard deviation of 6 yards.

A. What proportion of his drives exceed 280 yards in length?

B. How many yards should this golfer drive a ball so that the distance is among his longest 25%?

8. The average number of pounds of meat a person consumes a year is 212.3 pounds. Assume that the standard deviation is 20 pounds. If a sample of 50 individuals is selected, find the probability that the mean of the sample will be less than 210 pounds per year.

9. Suppose that a presidential candidate is favored by 51% of all eligible voters. What is the probability that in a random sample of 100 registered voters, less than 49% will favor that candidate?

A. The distance a student commutes from home to campus.

B. The rating of a stock as "strong buy," "buy," "hold," or "sell."

C. The percentage of alcohol (in volume) in Budweiser Beer.

2. A major airline wanted some information on those enrolled in their "frequent flyer" program. A sample of 10 members resulted in the following number of miles flown, to the nearest 1,000 miles, by each participant.

41, 22, 78, 54, 72, 97, 67, 64, 70, 55

A. Use 6 to 14 classes of equal width to create a table of frequencies for the "frequent flyer" data.

B. Draw a stem-and-leaf display for the "frequent flyer" data.

C. Find the first, second, and third quartiles of the "frequent flyer."

3. The following data consists of shoe sizes for six students:

9, 6.5, 8, 8.5, 7.5, 8.5

A. Find the mean shoe size for these six students.

B. Find the standard deviation of the shoe sizes.

4. The following table gives the two-way classification of 2,000 randomly selected employees from a city, based on gender and commuting time from home to work.

Commuting Time from Home to Work:

Less Than 30 Minutes 30 Minutes to One Hour More Than One Hour

Men: 524 455 221

Women: 413 263 124

_____________________________________________________

A. If one employee is selected at random from these 2,000 employees, find the probability that this employee

i. commutes for more than one hour.

ii. commutes for at least half an hour.

iii. commutes for at most one hour given that the employee is a woman.

B. (Are the events "man" and "commutes for more than one hour" independent? Explain.

5. The number of defects in a machine-made product is a random variable with the following probability distribution:

X P(x)

0 0.5

1 0.3

2 0.1

3 0.1

A. Find the probability that there are no more than 2 defects in a product.

B. Find the probability that the number of defects in a product is between 1 and 3, inclusive.

C. Find the probability that a randomly selected product has at most 1 defect.

D. Find the expected number of defects in a product.

E. Find the variance of the number of defects in a product.

6. Twenty percent of the patients treated by a new drug for AIDS show signs of improvement within six weeks. A random sample of five patients is selected and treated by the new drug.

A. Is this a binomial experiment?

B. Find the probability that 4 patients in the sample will show signs of improvement within six weeks.

7. The distance that one professional golfer can drive a golf ball has a normal distribution with a mean of 258 yards and a standard deviation of 6 yards.

A. What proportion of his drives exceed 280 yards in length?

B. How many yards should this golfer drive a ball so that the distance is among his longest 25%?

8. The average number of pounds of meat a person consumes a year is 212.3 pounds. Assume that the standard deviation is 20 pounds. If a sample of 50 individuals is selected, find the probability that the mean of the sample will be less than 210 pounds per year.

9. Suppose that a presidential candidate is favored by 51% of all eligible voters. What is the probability that in a random sample of 100 registered voters, less than 49% will favor that candidate?

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