Statistics Test Answers

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Question Description

The following frequency distribution shows the price per share for a sample of 30 companies listed on the New York Stock Exchange.

Price per ShareFrequency
$20-297
$30-395
$40-494
$50-594
$60-695
$70-791
$80-894

Compute the sample mean price per share and the sample standard deviation of the price per share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price per shares between 29 and 30, 39 and 40, etc.

Sample mean$
Sample standard deviation$

Consider the following data and corresponding weights.

xiWeight(wi)
3.97
3.04
3.51
3.09

a. Compute the weighted mean (to 3 decimals).

b. Compute the sample mean of the four data values without weighting (to 3 decimals).


Consider a sample with data values of 26, 24, 20, 16, 32, 34, 29, and 24. Compute the 20th, 25th, 65th, and 75th percentiles (to 1 decimal, if decimals are necessary).



20th percentile
25th percentile
65th percentile
75th percentile
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance.
City:17.317.81715.514.316.417.917.117.216.416.316.417.3
Highway:20.922.119.820.120.718.918.720.120.522.620.92020.2
Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal).
City Highway
Mean
Median
Mode


Make a statement about the difference in gasoline consumption between both driving conditions.

The National Sporting Goods Association conducted a survey of persons 7 years of age or older about participation in sports activities (Statistical Abstract of the United States: 2002). The total population in this age group was reported at 248.5 million, with 120.9 million male and 127.6 million female. The number of participants for the top five sports activities appears here.

Participants (millions)
ActivityMaleFemale
Bicycle riding23.719.5
Camping27.122.8
Exercise walking30.256.2
Exercising with equipment18.925.9
Swimming27.932.9



  1. For a randomly selected female, estimate the probability of participation in each of the sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of participation in more than one sports activity.
    Bicycle riding
    Camping
    Exercise walking
    Exercising with equipment
    Swimming

  2. For a randomly selected male, estimate the probability of participation in each of the sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of participation in more than one sports activity.
    Bicycle riding
    Camping
    Exercise walking
    Exercising with equipment
    Swimming

  3. For a randomly selected person, what is the probability the person participates in exercise walking (to 2 decimals)?

  4. Suppose you just happen to see an exercise walker going by. What is the probability the walker is a woman (to 2 decimals)?


    What is the probability the walker is a man (to 2 decimals)?

The following table provides a probability distribution for the random variable y.

yf(y)
20. 20
40. 30
70. 40
80. 10

a. Compute E(y) (to 1 decimal).

b. Compute Var(y) and σ (to 2 decimals).

Var(y)
σ



Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.



TABLE 4.2 COMPLETION RESULTS FOR 40 KP&L PROJECTS
Completion Time (months)
Stage 1
Design
Stage 2
Construction
Sample pointNumber of
Past Projects
Having These
Completion Times
27( 2, 7)
6
28( 2, 8)
4
29(2, 9)
2
37(3, 7)
4
38(3, 8)
6
39(3, 9)
2
47(4, 7)
4
48(4, 8)
4
49(4, 9)8
Total40



Table 4.3PROBABILITY ASSIGNMENTS FOR THE KP&L PROJECT BASED ON THE RELATIVE FREQUENCY METHOD
Sample pointProject
Completion Time
Probability
of Sample Point
(2, 7)9 monthsP(2, 7)=6/40=0.15
(2, 8)10 monthsP(2, 8)=4/40=0.1
(2, 9)11 monthsP(2, 9)=2/40=0.05
(3, 7)10 monthsP(3, 7)=4/40=0.1
(3, 8)11 monthsP(3, 8)=6/40=0.15
(3, 9)12 monthsP(3, 9)=2/40=0.05
(4, 7)11 monthsP(4, 7)=4/40=0.1
(4, 8)12 monthsP(4, 8)=4/40=0.1
(4, 9)13 monthsP(4, 9)=8/40=0.2
Total 1.00
  1. The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget.

  2. What is the probability that the design stage is over budget (to 2 decimal)?

  3. The construction stage (stage 2) will run over budget if it takes 9 months to complete. List the sample points in the event the construction stage is over budget.

  4. What is the probability that the construction stage is over budget (to 2 decimals)?

  5. What is the probability that both stages are over budget (to 2 decimals)?

Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:

2005 Season 7377787674727476
2006 Season 7069747684797078
  1. Calculate the mean (0 decimals) and the standard deviation (to 2 decimals) of the golfer's scores, for both years.
    2005
    Mean
    Standard deviation

    2006
    Mean
    Standard deviation

  2. What is the primary difference in performance between 2005 and 2006?


    What improvement, if any, can be seen in the 2006 scores?

The probability distribution for the random variable x follows.


xf(x)
200.24
240.19
320.27
350.30
  1. Is this a valid probability distribution?

  2. What is the probability that x = 32 (to 2 decimals)?

  3. What is the probability that x is less than or equal to 24 (to 2 decimals)?

  4. What is the probability that x is greater than 32 (to 2 decimals)?
Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
8,6601,4151,9289,1452,53311,755
62614,1386,6461,9062,9031,397
10,8137,7024,1404,4717612,191
3,7635,9688,554
  1. Provide a five-number summary. If needed, round your answer to a whole number.
    Smallest value
    First quartile
    Median
    Third quartile
    Largest value

  2. Compute the lower and upper limits. Enter negative amounts with a minus sign.
    Lower limit
    Upper limit

  3. Do the data contain any outliers?

  4. Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?

  5. Which of the following box plots accurately displays the data set?





    Consider a sample with a mean of 50 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
    1. 40 to 60, at least %
    2. 25 to 75, at least %
    3. 42 to 58, at least %
    4. 38 to 62, at least %
    5. 34 to 66, at least %

    Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.
    Undergraduate Major
    BusinessEngineeringOtherTotals
    Intended EnrollmentFull Time42039375888
    StatusPart Time402591451,038
    Totals8229841201,926

    1. Develop a joint probability table for these data (to 3 decimals).
      Undergraduate Major
      BusinessEngineeringOtherTotals
      Intended EnrollmentFull-Time
      StatusPart-Time
      Totals

    2. Use the marginal probabilities of undergraduate major (Business, Engineering, or Other) to comment on which undergraduate major produces the most potential MBA students.

    3. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate Engineering major (to 3 decimals)?

    4. If a student was an undergraduate Business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree (to 3 decimals)?

    5. Let A denote the event that student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate Business major. Are events A and B independent?

    Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.
    1. Compute the probability of no arrivals in a one-minute period (to 6 decimals).

    2. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals).

    3. Compute the probability of no arrivals in a 15-second period (to 4 decimals).

    4. Compute the probability of at least one arrival in a 15-second period (to 4 decimals).

    In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance.

    City:20.821.320.51917.819.921.420.620.719.919.819.920.8
    Highway:24.225.423.123.42422.22223.423.825.924.223.323.5
    Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal).



    City Highway
    Mean
    Median
    Mode



    Make a statement about the difference in gasoline consumption between both driving conditions.


    Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 50 employees; the Hawaii plant has 30. A random sample of 10 employees is to be asked to fill out a benefits questionnaire.

    Round your answers to four decimal places.

    a. What is the probability that none of the employees in the sample work at the plant in Hawaii?

    b. What is the probability that 1 of the employees in the sample works at the plant in Hawaii?

    c. What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii?

    d. What is the probability that 9 of the employees in the sample work at the plant in Texas?


    The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1 hours.

    Round your answers to the nearest whole number.
    1. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.9 and 8.9 hours.
      At least %
    2. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.
      At least %
    3. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.9 and 8.9 hours per day.
      %

      How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)?

    Consider the experiment of tossing a coin three times.
    1. How many experimental outcomes exist?

    2. Let x denote the number of heads occurring on three coin tosses. Show the value the random variable would have for each of the experimental outcomes.
      OutcomeValue of x
      (Tail, Tail, Tail)
      (Head, Tail, Tail)
      (Tail, Tail, Head)
      (Head, Tail, Head)
      (Tail, Head, Head)
      (Head, Head, Tail)
      (Head, Head, Head)
      (Tail, Head, Tail)
    3. Is this random variable discrete or continuous?

    A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 10% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 3% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
    1. What is the probability an employee will experience a lost-time accident in both years (to 3 decimals)?

    2. What is the probability an employee will experience a lost-time accident over the two-year period (to 3 decimals)?

    Many students accumulate debt by the time they graduate from college. Shown in the following table is the percentage of graduates with debt and the average amount of debt for these graduates at four universities and four liberal arts colleges.

    University% with DebtAmount($)College% with DebtAmount($)
    17932,96018328,752
    26732,16029229,000
    35811,22135310,203
    46411,85344411,013

    a. If you randomly choose a graduate of College 2, what is the probability that this individual graduated with debt (to 2 decimals)?

    b. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution with more than 90% of its graduates having debt (to 3 decimals)?

    c. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution whose graduates with debts have an average debt of more than $ 23,000 (to 3 decimals)?

    d. What is the probability that a graduate of University 1 does not have debt (to 2 decimals)?

    e. For graduates of University 1 with debt, the average amount of debt is $ 32,960. Considering all graduates from University 1, what is the average debt per graduate? Round to nearest dollar.
    $


    Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, ..., E7 denote the sample points. The following probability assignments apply:

    P(E1) = 0.1, P(E2) = 0.2, P(E3) = 0.1, P(E4) = 0.25, P(E5) = 0.15, P(E6) = 0.05, and P(E7) = 0.15.

    Assume the following events when answering the questions.

    1. Find P(A), P(B), and P(C).

      P(A)
      P(B)
      P(C)
    2. What is P(A B)?

    3. What is P(A B)?

    4. Are events A and C mutually exclusive?

    5. What is P(Bc )?

    When a new machine is functioning properly, only 2% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.

    a. Using the Figure 5.3, select a tree diagram that shows this problem as a two-trial experiment. Here D: defective; G: not defective.

    1.
    2.
    3.
    4.

    Choose the Correct option from the above tree diagrams:

    b. How many experimental outcomes result in exactly one defect being found?

    c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals).

    P (no defects)
    P (1 defect)
    P (2 defects)

    Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
    8,5761,4011,9109,0572,50811,641
    62114,1386,5811,8872,8741,383
    10,7087,6284,1004,4287542,170
    3,7265,9108,472
    1. Provide a five-number summary.
      Smallest value
      First quartile
      Median
      Third quartile
      Largest value

    2. Compute the lower and upper limits.
      Lower limit
      Upper limit

    3. Do the data contain any outliers?

    4. Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?

    5. Which of the following box plots accurately displays the data set?




    Figure 1.11 provides a bar chart showing the amount of federal spending for the years 2004 to 2010 (Congressional Budget Office website, May 15, 2011).

    FIGURE 1.11 FEDERAL SPENDING

    Year

    a. What is the variable of interest?

    b. Are the data categorical or quantitative?

    c. Are the data time series or cross-sectional?

    d. Comment on the trend in federal spending over time.


    How much did the federal government spend in 2007?
    $ trillions (to 1 decimal)


    Suppose that we have two events, A and B, with P(A) = .50, P(B) = .50, and P(A ∩ B) = .20.

    a. Find P(A | B) (to 4 decimals).

    b. Find P(B | A) (to 4 decimals).

    c. Are A and B independent? Why or why not?
    because P(A | B) P(A)


    Consider a binomial experiment with two trials and p =0.2.
    1. Which of the following tree diagrams accurately represents this binomial experiment?




    2. Compute the probability of one success, f(1) (to 2 decimals).

    3. Compute f(0) (to 2 decimals).

    4. Compute f(2) (to 2 decimals).

    5. Compute the probability of at least one success (to 2 decimals).

    6. Compute the following (to 2 decimals).
      Expected value
      Variance
      Standard deviation

                                Tutor Answer

                                mickeygabz
                                School: Carnegie Mellon University

                                See attached. Finishing up the rest

                                The following frequency distribution shows the price per share for a sample of 30 companies
                                listed on the New York Stock Exchange.
                                Price per Share
                                $20-29
                                $30-39
                                $40-49
                                $50-59
                                $60-69
                                $70-79
                                $80-89

                                Frequency
                                7
                                5
                                4
                                4
                                5
                                1
                                4

                                Compute the sample mean price per share and the sample standard deviation of the price per
                                share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price
                                per shares between 29 and 30, 39 and 40, etc.
                                Sample mean

                                $

                                Sample standard deviation $
                                Consider the following data and corresponding weights.
                                xi Weight(wi)
                                3.9 7
                                3.0 4
                                3.5 1
                                3.0 9
                                a. Compute the weighted mean (to 3 decimals).

                                b. Compute the sample mean of the four data values without weighting (to 3 decimals).

                                Consider a sample with data values of 26, 24, 20, 16, 32, 34, 29, and 24. Compute the 20th, 25th,
                                65th, and 75th percentiles (to 1 decimal, if decimals are necessary).

                                20th percentile
                                25th percentile
                                65th percentile
                                75th percentile
                                In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for
                                300 miles in both city and highway driving conditions. The following data were recorded for
                                miles-per-gallon performance.
                                City:
                                17.3 17.8 17 15.5 14.3 16.4 17.9 17.1 17.2 16.4 16.3 16.4 17.3
                                Highway: 20.9 22.1 19.8 20.1 20.7 18.9 18.7 20.1 20.5 22.6 20.9 20 20.2
                                Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1
                                decimal).
                                City
                                Highway
                                Mean
                                Median
                                Mode

                                20.9

                                Make a statement about the difference in gasoline consumption between both driving conditions.
                                Gasoline consumption is higher in highways as compared to city.

                                The National Sporting Goods Association conducted a survey of persons 7 years of age or older
                                about participation in sports activities (Statistical Abstract of the United States: 2002). The total
                                population in this age group was reported at 248.5 million, with 120.9 million male and 127.6
                                million female. The number of participants for the top five sports activities appears here.

                                Activity
                                Bicycle riding
                                Camping
                                Exercise walking
                                Exercising with equipment
                                Swimming

                                Participants (millions)
                                Male
                                Female
                                23.7
                                27.1
                                30.2
                                18.9
                                27.9

                                19.5
                                22.8
                                56.2
                                25.9
                                32.9

                                1. For a randomly selected female, estimate the probability of participation in each of the
                                sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of
                                participation in more than one sports activity.
                                Bicycle riding
                                Camping
                                Exercise walking
                                Exercising with equipment
                                Swimming
                                2.
                                3. For a randomly selected male, estimate the probability of participation in each of the
                                sports activities (to 2 decimals). Note that the probabilities do not sum to 1 because of
                                participation in more than one sports activity.
                                Bicycle riding
                                Camping
                                Exercise walking
                                Exercising with equipment
                                Swimming
                                4.
                                5. For a randomly selected person, what is the probability the person participates in exercise
                                walking (to 2 decimals)?
                                6. Suppose you just happen to see an exercise walker going by. What is the probability the
                                walker is a woman (to 2 decimals)?

                                What is the probability the walker is a man (to 2 decimals)?

                                The following table provides a probability distribution for the random variable y.
                                y f(y)
                                2 0. 20
                                4 0. 30
                                7 0. 40
                                8 0. 10

                                a. Compute E(y) (to 1 decimal).

                                b. Compute Var(y) and σ (to 2 decimals).
                                Var(y)
                                σ

                                Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.

                                TABLE 4.2 COMPLETION RESULTS FOR 40 KP&L PROJECTS
                                Completion Time (months)
                                Number of
                                Stage 1
                                Stage 2
                                Past Projects
                                Sample point
                                Design
                                Construction
                                Having These
                                Completion Times
                                2
                                7
                                ( 2, 7)
                                6
                                2
                                8
                                ( 2, 8)
                                4
                                2
                                9
                                (2, 9)
                                2
                                3
                                7
                                (3, 7)
                                4
                                3
                                8
                                (3, 8)
                                6
                                3
                                9
                                (3, 9)
                                2
                                4
                                7
                                (4, 7)
                                4
                                4
                                8
                                (4, 8)
                                4
                                4
                                9
                                (4, 9)
                                8
                                Total 40

                                Table 4.3
                                Sample
                                point
                                (2, 7)
                                (2, 8)
                                (2, 9)

                                PROBABILITY ASSIGNMENTS FOR THE KP&L PROJECT BASED ON THE
                                RELATIVE FREQUENCY METHOD
                                Project
                                Probability
                                Completion Time
                                of Sample Point
                                9 months
                                P(2, 7)=6/40=0.15
                                10 months
                                P(2, 8)=4/40=0.1
                                11 months
                                P(2, 9)=2/40=0.05

                                (3, 7)
                                (3, 8)
                                (3, 9)
                                (4, 7)
                                (4, 8)
                                (4, 9)

                                10 months
                                11 months
                                12 months
                                11 months
                                12 months
                                13 months

                                P(3, 7)=4/40=0.1
                                P(3, 8)=6/40=0.15
                                P(3, 9)=2/40=0.05
                                P(4, 7)=4/40=0.1
                                P(4, 8)=4/40=0.1
                                P(4, 9)=8/40=0.2
                                Total 1.00

                                1. The design stage (stage 1) will run over budget if it takes 4 months to complete. List the
                                sample points in the event the design stage is over budget.

                                (4, 7)
                                (4, 8)
                                (4, 9)


                                • What is the probability that the design stage is over budget (to 2 decimal)?
                                • The construction stage (stage 2) will run over budget if it takes 9 months to complete. List the
                                sample points in the event the construction stage is over budget.
                                (2, 9)
                                (3, 9)
                                (4, 9)

                                3. What is the probability that the construction stage is over budget (to 2 decimals)?
                                4. What is the probability that both stages are over budget (to 2 decimals)?

                                Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs,
                                Florida, during 2005 and 2006 are as follows:
                                2005 Season 73 77 78 76 74 72 74 76
                                2006 Season 70 69 74 76 84 79 70 78

                                1. Calculate the mean (0 decimals) and the standard deviation (to 2 decimals) of the golfer's
                                scores, for both years.
                                2005
                                Mean
                                Standard deviation
                                2006
                                Mean
                                Standard deviation
                                2.
                                3. What is the primary difference in performance between 2005 and 2006?

                                0
                                What improvement, if any, can be seen in the 2006 scores?
                                There were score above 80 in 2006
                                The probability distribution for the random variable x follows.

                                x f(x)
                                20 0.24
                                24 0.19
                                32 0.27
                                35 0.30
                                1. Is this a valid probability distribution?

                                YES
                                1.
                                2. What is the probability that x = 32 (to 2 decimals)?
                                3. What is the probability that x is less than or equal to 24 (to 2 decimals)?

                                4. What is the probability that x is greater than 32 (to 2 decimals)?

                                Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
                                8,660 1,415 1,928 9,145 2,533 11,755
                                626 14,138 6,646 1,906 2,903 1,397
                                10,813 7,702 4,140 4,471 761 2,191
                                3,763 5,968 8,554
                                1. Provide a five-number summary. If needed, round your answer to a whole number.
                                Smallest value
                                First quartile
                                Median
                                Third quartile
                                Largest value
                                2.
                                3. Compute the lower and upper limits. Enter negative amounts with a minus sign.
                                Lower limit
                                Upper limit
                                4.
                                5. Do the data contain any outliers?

                                No

                                • Johnson & Johnson's sales are the largest on the list at $14,138 million. Suppose a data entry
                                error (a transposition) had been made and the sales had been entered as $41,138 million. Would
                                the method of detecting outliers in part (c) identify this problem and allow for correction of the
                                data entry error?
                                Yes. The value would be identified as an outlier.
                                • Which of the following box plots accu...

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                                Review

                                Anonymous
                                awesome work thanks

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