# Statistics Test Answers The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 63 A, 22 B, and 35 C. Show the f

Statistics Test Answers The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 63 A, 22 B, and 35 C. Show the frequency and relative frequency distributions (use nearest whole number for the frequency column and 2 decimal for the relative frequency column).

Class Frequency Relative Frequency

A

B

C

(Total)

A bowler’s scores for six games were 182, 168, 185, 196, 172, and 176. Using these data as a sample, compute the following descriptive statistics:

a. Range

b. Variance (to 1 decimal)

c. Standard deviation (to 2 decimals)

d. Coefficient of variation (to 2 decimals) %

The Canmark Research Center Airport Customer Satisfaction Survey uses an online questionnaire to provide airlines and airports with customer satisfaction ratings for all aspects of the customers’ flight experience. After completing a flight, customers receive an email asking them to go to the website and rate a variety of factors, including the reservation process, the check-in process, luggage policy, cleanliness of gate area, service by flight attendants, food/beverage selection, on-time arrival, and so on. A five-point scale, with Excellent (E), Very Good (V), Good (G), Fair (F), and Poor (P), is used to record the customer ratings for each survey question. Assume that passengers on a Delta Airlines flight from Myrtle Beach, South Carolina, to Atlanta, Georgia, provided the following ratings for the question, “Please rate the airline based on your overall experience with this flight.” The sample ratings are shown below.

V V G V V E V V V E

E G V E E V E E E V

V V V F V E V E G E

G E V E V E V V V V

E E V V E P E V P V

a. Use a percent frequency distribution and the following bar charts:

1.

Customer Rating

2.

Customer Rating

3.

Customer Rating

4.

Customer Rating

Select the correct bar chart.

– Select your answer –

Bar chart 1

Bar chart 2

Bar chart 3

Bar chart 4

Item 1

To summarize the above data.

Rating Frequency Percent Frequency

Excellent

Very Good

Good

Fair

Poor

Total

What do these summaries indicate about the overall customer satisfaction with the Delta flight?

% of customers are satisfied with the Delta flight at either a good, very good, or excellent rating. Only % of customers rated the Delta flight Fair or Poor.

b. The online survey questionnaire enabled respondents to explain any aspect of the flight that failed to meet expectations. Would this be helpful information to a manager looking for ways to improve the overall customer satisfaction on Delta flights? Explain.

Allowing survey respondents to explain their 5-point scale responses would provide helpful information to managers looking for ways to improve customer satisfaction on Delta flights. The % respondents indicating that the flight failed to meet expectations would have the opportunity to provide detailed information about their expectations.

Consider a sample with a mean of 40 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).

20 to 60, at least %

25 to 55, at least %

31 to 49, at least %

28 to 52, at least %

22 to 58, at least %

In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 55% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 83% take prescription drugs regularly. For adults age 18 to 64, 47% take prescription drugs regularly. The age 18–64 age group accounts for 87.4% of the adult population (Statistical Abstract of the United States, 2008).

Round your answers to 4 decimal places.

a. What is the probability that a randomly selected adult is 65 or older?

b. Given an adult takes prescription drugs regularly, what is the probability that the adult is 65 or older?

The prior probabilities for events A1 and A2 are P(A1) = .50 and P(A2) = .50. It is also known that P(A1 A2) = 0. Suppose P(B | A1) = .20 and P(B | A2) = .08.

Are events A1 and A2 mutually exclusive?

Select

Yes

No

Item 1

Compute P(A1 B) (to 4 decimals).

Compute P(A2 B) (to 4 decimals).

Compute P(B) (to 4 decimals).

Apply Bayes’ theorem to compute P(A1 | B) (to 4 decimals).

Also apply Bayes’ theorem to compute P(A2 | B) (to 4 decimals).

Three students scheduled interviews for summer employment at an Institute. In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews.

How many experimental outcomes exist?

Let x equal the number of students who receive an offer. Is x continuous or discrete?

Select

It is discrete

It is continuous

It is neither discrete nor continuous

Item 2

Show the value of the random variable x, where x is the number of yeses. Let Y= “Yes, the student receives an offer”, and N = “No, the student does not receive an offer.”

Experimental Outcome Value of x

(N, Y, Y)

(N, N, Y)

(Y, Y, Y)

(N, N N)

(Y, Y, N)

(N, Y, N)

(Y, N, Y)

(Y, N, N)

The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.29, 0.2, 0.21, 0.11, and 0.19.

Show the probability distribution for the expense forecast.

x f(x)

9

10

11

12

13

What is the expected value of the expense forecast for the coming year (to 2 decimals)?

What is the variance of the expense forecast for the coming year (to 2 decimals)?

If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?

A doctor’s office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period.

5 9 10 15 5 4

4 19 12 7 6 6 14 21 7 9 7 13 16 4

Fill in the frequency (to the nearest whole number) and the relative frequency (2 decimals) values below.

Waiting Time Frequency Relative Frequency

0-4

5-9

10-14

15-19

20-24

(Total)

Fill in the cumulative frequency (to the nearest whole number) and the cumulative relative frequency (2 decimals) values below.

Waiting Time Cumulative Frequency Cumulative Relative Frequency

Less than or equal to 4

Less than or equal to 9

Less than or equal to 14

Less than or equal to 19

Less than or equal to 24

What proportion of patients needing emergency service wait 14 minutes or less?

Consider the random experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability.

How many sample points are there in the event that a jack is selected?

How many sample points are there in the event that a club is selected?

How many sample points are there in the event that a face card ( jack, queen, or king) is selected?

Find the probabilities associated with each of the events in parts (a), (b), and (c) (to 2 decimals).

(a) Ace

(b) Club

(c) Face card

The number of students taking the SAT has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows.

Number of

Times Number of

Students

1 777,000

2 649,000

3 179,000

4 22,000

5 19,100

a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable. Round your answers to four decimal places.

x f(x)

1

2

3

4

5

b. What is the probability that a student takes the SAT more than one time? Round your answer to four decimal places.

c. What is the probability that a student takes the SAT three or more times? Round your answer to four decimal places.

d. What is the expected value of the number of times the SAT is taken? Round your interim calculations and final answer to four decimal places.

What is your interpretation of the expected value?

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

e. What is the variance and standard deviation for the number of times the SAT is taken? Round your interim calculations and final answer to four decimal places.

Variance

Standard deviation

A questionnaire provides 63 Yes, 39 No, and 18 no-opinion answers.

In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers?

degrees

How many degrees would be in the section of the pie showing the No answers?

degrees

If you constructed a pie chart, what percentage of the circle that would be occupied by each response. Round answers to one decimal place.

Yes %

No %

No Opinion %

Which of the following three bar graphs accurately represents the data?

1.

Response

2.

Response

3.

Response

Select

Graph #1

Graph #2

Graph #3

None of these three graphs

Item 6

The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample data consistent with the NHTSA survey are as follows.

Driver Using Seat Belt?

Region

Yes

No

Northeast

150

55

Midwest

164

51

South

296

74

West

254 51

Total

864 231

Combining the results from all four regions, what is the probability that a U.S. driver is using a seat belt (to 2 decimals)?

The seat belt usage probability for a U.S. driver a year earlier was .75. NHTSA chief Dr. Jeffrey Runge had hoped for a .78 probability in 2003. Would he have been pleased with the 2003 survey results?

– Select your answer –

Yes, because his expectations were exceeded

No, because his expectations were not met

Item 2

What is the probability of seat belt usage by region of the country (to 2 decimals)?

Northeast

Midwest

South

West

What region has the highest probability of seat belt usage? (to 2 decimals)

– Select your answer –

Northeast

Midwest

South

West

Item 7

The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.29, 0.16, 0.24, 0.13, and 0.18.

Show the probability distribution for the expense forecast.

x f(x)

9

10

11

12

13

What is the expected value of the expense forecast for the coming year (to 2 decimals)?

What is the variance of the expense forecast for the coming year (to 2 decimals)?

If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?

The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 14 credit hours of B, 32 credit hours of C, and 5 credit hours of D.

a. Compute the student’s grade point average. Round your answer to two decimal places.

b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?

Select

Yes

No

Item 2

Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 95 bank accounts, we want to take a random sample of six accounts in order to learn about the population. How many different random samples of six accounts are possible?