# Stats - Midterm

hotjpka691.

A local restaurant is committed to providing its patrons with the best dining experience possible. On a recent survey, the restaurant asked patrons to rate the quality of their entrées. The responses ranged from 1 to 5, where 1 indicated a disappointing entrée and 5 indicated an exceptional entrée.

The results of the survey are as follows:

2 5 1 5 1 5 4 3 3 3 1 2

1 2 2 3 1 4 4 1 2 3 1 1

4 5 1 1 1 3 1 2 1 4 2 2

PictureClick here for the Excel Data File

a.

Construct frequency and relative frequency distributions that summarize the survey’s results. (Do not round intermediate calculations. Round "relative frequency" to 3 decimal places.)

Rating Frequency Relative

Frequency

5

4

3

2

1

Total

b.

Are patrons generally satisfied with the quality of their entrées?

No

Yes

rev: 07_05_2013_QC_32367, 03_04_2014_QC_44527

2.

Consider the following data set:

1 10 5 6 8 8 10 12 15 12

8 11 8 4 3 9 12 3 10 8

8 12 4 4 4 12 10 6 11 6

7 -6 31 16 -3 9 13 6 5 -4

29 -3 5 3 24 24 10 23 32 2

-5 -4 -2 14 -2 35 26 10 18 28

5 3 -6 7 28 36 16 3 -4 5

a-1. Construct a frequency distribution using classes of −10 up to 0, 0 up to 10, etc.

Classes Frequency

–10 up to 0

0 up to 10

10 up to 20

20 up to 30

30 up to 40

Total

a-2. How many of the observations are at least 10 but less than 20?

Number of observations

b-1.

Construct a relative frequency distribution and a cumulative relative frequency distribution. (Round "relative frequency" and "cumulative relative frequency" to 3 decimal places.)

Class Relative

Frequency Cumulative

Relative Frequency

–10 up to 0

0 up to 10

10 up to 20

20 up to 30

30 up to 40

Total

b-2.

What percent of the observations are at least 10 but less than 20? (Round your answer to 1 decimal place.)

Percent of observations %

b-3. What percent of the observations are less than 20? (Round your answer to 1 decimal place.)

Percent of observations %

c. Is the distribution symmetric? If not, then how is it skewed?

Not symmetric, skewed to right

Symmetric or Skewed to left

rev: 07_05_2013_QC_32367

3.

Assume that X is a binomial random variable with n = 16 and p = 0.66. Calculate the following probabilities. (Round your intermediate and final answers to 4 decimal places.)

a. P(X = 15)

b. P(X = 14)

c. P(X ≥ 14)

rev: 04_26_2013_QC_29765; rev: 08_07_20

4.

A professor of management has heard that twelve students in his class of 52 have landed an internship for the summer. Suppose he runs into two of his students in the corridor.

a.

Find the probability that neither of these students has landed an internship. (Round your intermediate calculations and final answer to 4 decimal places.)

formula176.mml

b.

Find the probability that both of these students have landed an internship. (Round your intermediate calculations and final answer to 4 decimal places.)

P(T1 ∩ T2)

rev: 08_06_2013_QC_32707

5.

Market observers are quite uncertain whether the stock market has bottomed out from the economic meltdown that began in 2008. In an interview on March 8, 2009, CNBC interviewed two prominent economists who offered differing views on whether the U.S. economy was getting stronger or weaker. An investor not wanting to miss out on possible investment opportunities considers investing $15,000 in the stock market. He believes that the probability is 0.25 that the market will improve, 0.42 that it will stay the same, and 0.33 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $23,000, but it can also go down to $10,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $15,000.

a.

What is the expected value of his investment?

Expected value $

b.

What should the investor do if he is risk neutral?

Investor

invest the $15,000.

c. Is the decision clear-cut if he is risk averse?

Yes

No

rev: 08_07_2013_QC_33420, 11_01_2013_QC_37895

6.

An investment strategy has an expected return of 12 percent and a standard deviation of 8 percent. Assume investment returns are bell shaped.

a.

How likely is it to earn a return between 4 percent and 20 percent? (Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Probability

b.

How likely is it to earn a return greater than 20 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Probability

c.

How likely is it to earn a return below −4 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Probability

rev: 02_26_2014_QC_44958, 07_12_2014_QC_51377

7.

Consider the following frequency distribution:

Class Frequency

10 up to 20 21

20 up to 30 22

30 up to 40 33

40 up to 50 12

a.

Construct a relative frequency distribution. (Round your answers to 3 decimal places.)

Class Relative

Frequency

10 up to 20

20 up to 30

30 up to 40

40 up to 50

Total

b.

Construct a cumulative frequency distribution and a cumulative relative frequency distribution. (Round "cumulative relative frequency" to 3 decimal places.)

Class Cumulative

Frequency Cumulative Relative

Frequency

10 up to 20

20 up to 30

30 up to 40

40 up to 50

c-1.

What percent of the observations are at least 20 but less than 30? (Round your answer to 1 decimal place.)

Percent of observations

c-2.

What percent of the observations are less than 20? (Round your answer to 1 decimal place.)

Percent of observations

rev: 07_05_2013_QC_32367, 08_12_2013_QC_33620

8.

Scores on the final in a statistics class are as follows.

68 24 70 56 72 76 74 116 87 55

82 88 54 66 64 58 84 60 79 62

PictureClick here for the Excel Data File

a.

Calculate the 25th, 50th, and 75th percentiles. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

25th percentile

50th percentile

75th percentile

b-1.

Calculate the IQR, lower limit and upper limit to detect outliers. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

IQR

Lower limit

Upper limit

b-2. Are there any outliers?

Yes

No

rev: 07_31_2013_QC_32713, 09_13_2013_QC_34880, 10_31_2013_QC_38175, 03_03_2014_QC_44705, 09_24_2014_QC_54188

9.

The estimation of which of the following requires sampling?

Total rainfall in Phoenix, Arizona, in 2010

The average SAT score of incoming freshmen at a university

U.S. unemployment rate

The Cleveland Indians' hitting percentage in 2010

10.

A researcher conducts a mileage economy test involving 79 cars. The frequency distribution describing average miles per gallon (mpg) appears in the following table.

Average mpg Frequency

15 up to 20 7

20 up to 25 15

25 up to 30 14

30 up to 35 27

35 up to 40 12

40 up to 45 4

a.

Construct the corresponding relative frequency, cumulative frequency, and cumulative relative frequency distributions. (Round "relative frequency" and "cumulative relative frequency" to 4 decimal places.)

Average mpg

Relative

Frequency

Cumulative

Frequency

Cumulative

Relative Frequency

15 up to 20

20 up to 25

25 up to 30

30 up to 35

35 up to 40

40 up to 45

Total

b-1. How many of the cars got less than 20 mpg?

Number of cars

b-2.

What percent of the cars got at least 25 but less than 30 mpg? (Round your answer to 2 decimal places.)

Percentage of cars

b-3.

What percent of the cars got less than 30 mpg? (Round your answer to 2 decimal places.)

Percentage of cars

b-4. What percent got 30 mpg or more? (Round your answer to 2 decimal places.)

Percentage of cars

rev: 07_05_2013_QC_32367

11.

Consider the following joint probability table.

B1 B2 B3 B4

A 0.14 0.10 0.15 0.09

Ac 0.15 0.17 0.10 0.10

PictureClick here for the Excel Data File

a. What is the probability that A occurs? (Round your answer to 2 decimal places.)

Probability

b. What is the probability that B2 occurs? (Round your answer to 2 decimal places.)

Probability

c. What is the probability that Ac and B4 occur? (Round your answer to 2 decimal places.)

Probability

d. What is the probability that A or B3 occurs? (Round your answer to 2 decimal places.)

Probability

e.

Given that B2 has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answers to 4 decimal places.)

Probability

f.

Given that A has occurred, what is the probability that B4 occurs? (Round your intermediate calculations and final answers to 4 decimal places.)

Probability

rev: 08_06_2013_QC_32707

12.

Consider the following cumulative relative frequency distribution.

Class Cumulative

Relative

Frequency

150 up to 200 0.19

200 up to 250 0.26

250 up to 300 0.55

300 up to 350 1.00

a-1. Construct a relative frequency distribution. (Round your answers to 2 decimal places.)

Class Relative

Frequency

150 up to 200

200 up to 250

250 up to 300

300 up to 350

Total

a-2. What percent of the observations are at least 250 but less than 300?

Percent of observations

13.

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 53% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 23%. There is only a 63% chance that she will find a tutor at such short notice.

a.

What is the probability that Christine fails the course? (Round your answer to 4 decimal places.)

Probability

b.

Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.)

Probability

rev: 08_06_2013_QC_32707

14.

A 2010 poll conducted by NBC asked respondents who would win Super Bowl XLV in 2011. The responses by 20,925 people are summarized in the following table.

Team Number of Votes

Atlanta Falcons 4,100

New Orleans Saints 1,860

Houston Texans 1,900

Dallas Cowboys 1,641

Minnesota Vikings 1,500

Indianapolis Colts 1,159

Pittsburgh Steelers 1,155

New England Patriots 1,106

Green Bay Packers 1,087

Others

a.

How many responses were for “Others”?

Number of responses

b.

The Green Bay Packers won Super Bowl XLV, defeating the Pittsburgh Steelers by the score of 31–25. What proportion of respondents felt that the Green Bay Packers would win? (Round your answer to 3 decimal places.)

Proportion of respondents

rev: 07_05_2013_QC_32367

15.

Consider the following population data:

37 41 14 11 23

a. Calculate the range.

Range

b.

Calculate MAD. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

MAD

c.

Calculate the population variance. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population variance

d.

Calculate the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population standard deviation

rev: 07_31_2013_QC_32713

16.

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.

Grade Numerical Score Probability

A 4 0.100

B 3 0.240

C 2 0.430

D 1 0.125

F 0 0.105

Part (a) omitted

b.

Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

Grade P(X ≤ x)

F

D

C

B

A

c.

What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Probability

d.

What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Probability

rev: 02_28_2014_QC_45290

17.

A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 55% chance that the player will miss both shots, a 25% chance that he will make one of the shots, and a 20% chance that he will make both shots.

a.

Construct the appropriate probability distribution. (Round your answers to 2 decimal places.)

x P(X = x)

0

1

2

b.

What is the probability that he makes no more than one of the shots? (Round your answer to 2 decimal places.)

Probability

c.

What is the probability that he makes at least one of the shots? (Round your answer to 2 decimal places.)

Probability

rev: 09_13_2013_QC_35141

18.

Records show that 13% of all college students are foreign students who also smoke. It is also known that 50% of all foreign college students smoke. What percent of the students at this university are foreign?

Percent of the students %

19.

Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities.

a.

Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails.

Subjective probability

Empirical probability

Classical probability

b.

At the beginning of the semester, John believes he has a 90% chance of receiving straight A’s.

Subjective probability

Empirical probability

Classical probability

c.

A political reporter announces that there is a 48% chance that the next person to come out of the conference room will be a Republican, since there are 85 Republicans and 91 Democrats in the room.

Subjective probability

Empirical probability

Classical probability

20.

A data set has a mean of 1,080 and a standard deviation of 80.

a.

Using Chebyshev's theorem, what percentage of the observations fall between 760 and 1,400? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Percentage of observations

b.

Using Chebyshev’s theorem, what percentage of the observations fall between 920 and 1,240? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Percentage of observations

rev: 07_31_2013_QC_32713

21.

Let P(A) = 0.62, P(B) = 0.27, and P(A ∩ B) = 0.17.

a. Calculate P(A | B). (Round your answer to 2 decimal places.)

P(A | B)

b. Calculate P(A U B). (Round your answer to 2 decimal places.)

P(A U B)

c. Calculate P((A U B)c). (Round your answer to 2 decimal places.)

P((A U B)c)

rev: 08_06_2013_QC_32707

22.

Let P(A) = 0.51, P(B | A) = 0.36, and P(B | Ac) = 0.14. Use a probability tree to calculate the following probabilities: (Round your answers to 3 decimal places.)

a. P(Ac)

b. P(A ∩ B)

P(Ac ∩ B)

c. P(B)

d. P(A | B)

rev: 08_06_2013_QC_32707, 10_09_2014_QC_55407

23.

Consider the following observations from a population:

133 240 38 93 93 26 184 108 38

PictureClick here for the Excel Data File

a. Calculate the mean and median. (Round "mean" to 2 decimal places.)

Mean

Median

b.

Select the mode. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.)

240

26

108

133

38

93

184

rev: 07_31_2013_QC_32713

24.

An analyst thinks that next year there is a 40% chance that the world economy will be good, a 10% chance that it will be neutral, and a 50% chance that it will be poor. She also predicts probabilities that the performance of a start-up firm, Creative Ideas, will be good, neutral, or poor for each of the economic states of the world economy. The following table presents probabilities for three states of the world economy and the corresponding conditional probabilities for Creative Ideas.

State of

the World

Economy Probability

of Economic

State Performance

of Creative

Ideas Conditional

Probability of

Creative Ideas

Good 0.40 Good 0.20

Neutral 0.30

Poor 0.50

Neutral 0.10 Good 0.40

Neutral 0.10

Poor 0.50

Poor 0.50 Good 0.40

Neutral 0.40

Poor 0.20

PictureClick here for the Excel Data File

a.

What is the probability that the performance of the world economy will be neutral and that of creative ideas will be poor? (Round your answer to 2 decimal places.)

Probability

b.

What is the probability that the performance of Creative Ideas will be poor? (Round your answer to 2 decimal places.)

Probability

c.

The performance of Creative Ideas was poor. What is the probability that the performance of the world economy had also been poor? (Round your answer to 2 decimal places.)

Probability

rev: 08_06_2013_QC_32707

25.

Complete the following probability table. (Round Prior Probability answers to 2 decimal places and intermediate calculations and other answers to 4 decimal places.)

Prior

Probability Conditional Probability Joint

Probability Posterior

Probability

P(B) 0.53 P(A | B) 0.15 P(A ∩ B ) P(B | A)

P(Bc) P(A | Bc) 0.38 P(A ∩ Bc) P(Bc | A)

Total P(A) Total

rev: 08_06_2013_QC_32707

26.

Consider the following sample data:

x 8 10 7 5 2

y 11 2 7 4 8

a.

Calculate the covariance between the variables. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Covariance

b-1.

Calculate the correlation coefficient. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Correlation coefficient

b-2. Interpret the correlation coefficient.

There is

relationship between x and y.

rev: 07_31_2013_QC_32713

27.

India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution of the household size in India.

Household Size Probability

1 0.04

2 0.12

3 0.18

4 0.24

5 0.13

6 0.15

7 0.10

8 0.04

a.

What is the probability that there are less than 5 members in a typical household in India? (Round your answer to 2 decimal places.)

Probability

b.

What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)

Probability

c.

What is the probability that the number of members in a typical household in India is greater than 4 and less than 7 members? (Round your answer to 2 decimal places.)

Probability

rev: 02_26_2014_QC_45094

28.

The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ± one-mile-per-hour accuracy 70% of the time; that is, there is a 0.70 probability that the gun will detect a speeder, if the driver is actually speeding. Assume there is a 2% chance that the gun erroneously detects a speeder even when the driver is below the speed limit. Suppose that 67% of the drivers drive below the speed limit on this stretch of the Massachusetts Turnpike.

a.

What is the probability that the gun detects speeding and the driver was speeding? (Round your answer to 4 decimal places.)

Probability

b.

What is the probability that the gun detects speeding and the driver was not speeding? (Round your answer to 4 decimal places.)

Probability

c.

Suppose the police stop a driver because the gun detects speeding. What is the probability that the driver was actually driving below the speed limit? (Round your answer to 4 decimal places.)

Probability

rev: 08_06_2013_QC_32707

29.

At a local bar in a small Midwestern town, beer and wine are the only two alcoholic options. The manager noted that of all male customers who visited over the weekend, 153 ordered beer, 46 ordered wine, and 17 asked for soft drinks. Of female customers, 37 ordered beer, 23 ordered wine, and 10 asked for soft drinks.

a.

Construct a contingency table that shows frequencies for the qualitative variables Gender (male or female) and Drink Choice (beer, wine, or soft drink).

Drink Choice

Gender Beer (B) Wine (W) Soft Drinks (D) Totals

Male (M)

Female (F)

Total

b. Find the probability that a customer orders wine. (Round your intermediate calculations and final answer to 4 decimal places.)

P(W)

c.

What is the probability that a male customer orders wine? (Round your intermediate calculations and final answer to 4 decimal places.)

P (W | M )

d. Are the events “Wine” and “Male” independent?

Yes because P(“Wine” | “Male”) = P(“Wine”).

Yes because P(“Wine” ∩ “Male”) = P(“Wine”).

No because P(“Wine” | “Male”) ≠ P(“Wine”).

No because P(“Wine” ∩ “Male”) ≠ P(“Wine”).

rev: 08_06_2013_QC_32707

30.

Consider the following frequency distribution.

Class Frequency

2 up to 4 21

4 up to 6 59

6 up to 8 81

8 up to 10 21

a.

Calculate the population mean. (Round your answer to 2 decimal places.)

Population mean

b.

Calculate the population variance and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Population variance

Population standard deviation

rev: 07_31_2013_QC_32713

31.

Which of the following variables is not continuous?

Time of a flight between Atlanta and Chicago

Height of NBA players

The number of obtained heads when a fair coin is tossed 20 times

Average temperature in the month of July in Orlando

32.

The one-year return (in %) for 24 mutual funds is as follows:

–10.7 –1.4 0.9 6.1 –15.9 –7.5

21.5 –9.6 4.5 11.1 14.5 4.7

–8.4 –8.4 19.5 14.9 29.3 7.7

22.0 24.8 –0.4 11.1 5.0 –11.0

PictureClick here for the Excel Data File

a.

Construct a frequency distribution using classes of –20 up to –10, –10 up to 0, etc.

Class (in %) Frequency

–20 up to –10

–10 up to 0

0 up to 10

10 up to 20

20 up to 30

Total

b.

Construct the relative frequency, the cumulative frequency, and the cumulative relative frequency distributions. (Round "relative frequency" and "cumulative relative frequency" answers to 3 decimal places.)

Class (in %) Relative

Frequency Cumulative

Frequency Cumulative

Relative Frequency

–20 up to –10

–10 up to 0

0 up to 10

10 up to 20

20 up to 30

Total

c-1. How many of the funds had returns of at least 20% but less than 30%?

Number of funds

c-2. How many of the funds had returns of 0% or more?

Number of funds

d-1.

What percent of the funds had returns of at least –10% but less than 0%? (Round your answer to 1 decimal place.)

Percent of funds

d-2.

What percent of the funds had returns less than 20%? (Round your answer to 1 decimal place.)

Percent of funds

rev: 06_24_2013_QC_31991, 07_05_2013_QC_32367

©2015 McGraw-Hill Education. All rights reserved.

33.

Investment advisors recommend risk reduction through international diversification. International investing allows you to take advantage of the potential for growth in foreign economies, particularly in emerging markets. Janice Wong is considering investment in either Europe or Asia. She has studied these markets and believes that both markets will be influenced by the U.S. economy, which has a 16% chance for being good, a 57% chance for being fair, and a 27% chance for being poor. Probability distributions of the returns for these markets are given in the accompanying table.

State of the

U.S. Economy Returns

in Europe Returns

in Asia

Good 14% 28%

Fair 5% 7%

Poor −12% −10%

a.

Find the expected value and the standard deviation of returns in Europe and Asia. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Europe Asia

Expected value % %

Standard deviation

b. What will Janice pick as an investment if she is risk neutral?

Investment in Europe

Investment in Asia

rev: 08_07_2013_QC_33420

34.

Consider the following probabilities: P(Ac) = 0.32, P(B) = 0.58, and P(A ∩ Bc) = 0.25.

a. Find P(A | Bc). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

P(A | Bc)

b. Find P(Bc | A). (Do not round intermediate calculations. Round your answer to 3 decimal places.)

P(Bc | A)

c. Are A and B independent events?

Yes because P(A | Bc) = P(A).

Yes because P(A ∩ Bc) ≠ 0.

No because P(A | Bc) ≠ P(A).

No because P(A ∩ Bc) ≠ 0.

rev: 08_06_2013_QC_32707

35.

The probabilities that stock A will rise in price is 0.64 and that stock B will rise in price is 0.36. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.56.

a.

What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.)

Probability

b. Are events A and B mutually exclusive?

Yes because P(A | B) = P(A).

Yes because P(A ∩ B) = 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

c. Are events A and B independent?

Yes because P(A | B) = P(A).

Yes because P(A ∩ B) = 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

rev: 08_06_2013_QC_32707

36.

A sample of patients arriving at Overbrook Hospital’s emergency room recorded the following body temperature readings over the weekend:

102.6 99.8 100.7 100.9 100.5 102.4 101.3 99.2 100.5 100.9

99.8 100.3 99.8 100.5 100.9 100.7 100.3 100.2 99.6 99.7

PictureClick here for the Excel Data File

a. Construct a stem-and-leaf diagram.

Stem Leaf

b. Interpret the stem-and-leaf diagram.

The distribution is Positively Skewed.

The distribution is Negatively Skewed.

The distribution is symmetric.

37.

A professor has learned that nine students in her class of 24 will cheat on the exam. She decides to focus her attention on eleven randomly chosen students during the exam.

a.

What is the probability that she finds at least one of the students cheating? (Round your intermediate calculations and final answers to 4 decimal places.)

Probability

b.

What is the probability that she finds at least one of the students cheating if she focuses on twelve randomly chosen students? (Round your intermediate calculations and final answers to 4 decimal places.)

Probability

rev: 08_07_2013_QC_33420

38.

At the end of a semester, college students evaluate their instructors by assigning them to one of the following categories: Excellent, Good, Average, Below Average, and Poor. The measurement scale is a(n) ____________.

nominal scale

ratio scale

ordinal scale

interval scale

39.

Consider the following contingency table.

B Bc

A 23 21

Ac 30 26

a.

Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)

B

Bc

Total

A

Ac

Total

b. What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

c. What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

d.

Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

e.

Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

f. Are A and B mutually exclusive events?

Yes because P(A | B) ≠ P(A).

Yes because P(A ∩ B) ≠ 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

g. Are A and B independent events?

Yes because P(A | B) ≠ P(A).

Yes because P(A ∩ B) ≠ 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.