Jan 9, 2017

Probability Distribution — practice test 5C

20 cards
, 56 answers
    Problems with solutions in Elementary Statistics — Random Variables; Binomial Probability Distributions: Mean, Variance, and Standard Deviation for the Binomial Distribution; The Poisson Distribution.

    Directions:
    Give your answers to the short-answer items. Choose the correct answer for multiple-choice items.

  • Provide an appropriate response.
    • 1. Compare the probability histogram for the expected sum with the actual results. What do you conclude about the dice results displayed in the Actual Sum of Two Dice histogram?



      Possible answer
      Based on the expected and actual results, at least one of the two dice must not be fair.

      1. 2. Describe the differences in the Poisson and the binomial distribution.

        Possible answer
        The Poisson computes probabilities for occurrences of events over some interval.
        The Poisson distribution is affected only by the mean μ, whereas the binomial is affected by sample size n and probability p.
        The Poisson distribution has discrete values from 1, 2, 3, … with no upper limit. A binomial distribution has discrete values from 1, 2, 3, to n; that is, the upper limit of values is n.

      2. Identify the given random variable as being discrete or continuous.
        • 3. The number of oil spills occurring off the Alaskan coast.
          1. Continuous
          2. Discrete

        • 4. The braking time of a car.
          1. Discrete
          2. Continuous

      3. Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
        • 5.

          Possible answer
          Not a probability distribution. The sum of the P(x)’s is not 1, since 1.088 ≠ 1.000

          1. 6. In a certain town, 20% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree.


            Possible answer
            Probability distribution.

          2. Find the mean of the given probability distribution.
            • 7. In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree.
              1. 2.30
              2. 2.40
              3. 2.00
              4. 2.43

            • 8. In a certain town, 30% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the standard deviation for the probability distribution.
              1. 1.51
              2. 0.92
              3. 1.06
              4. 0.84

            • 9. The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one:
              $3800 (1 chance in 8300);
              $2600 (1 chance in 6900);
              $800 (1 chance in 3000);
              $300 (1 chance in 2300).
              Find the expected value of the amount won for one entry if the cost to enter is 70 cents.
              1. $1.23
              2. $0.53
              3. $299.30
              4. $0.40

            • 10. Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table.

              Find the probability of selecting 12 or more girls.
              1. 0.022
              2. 0.006
              3. 0.001
              4. 0.007

          3. Answer the question.
            • 11. Suppose that weight of adolescents in being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are considered morbidly obese. Is it unusual to have no obese subjects among three randomly selected adolescents?
              1. Yes
              2. No

          4. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
            • 12. Rolling a single “loaded” die 39 times, keeping track of the “fives” rolled.
              1. Not binomial: there are too many trials.
              2. Procedure results in a binomial distribution.
              3. Not binomial: there are more than two outcomes for each trial.
              4. Not binomial: the trials are not independent.

          5. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
            • 13. n = 12, x = 5, p = 0.25
              1. 0.082
              2. 0.027
              3. 0.103
              4. 0.091

          6. Find the indicated probability.
            • 14. An airline estimates that 90% of people booked on their flights actually show up. If the airline books 71 people on a flight for which the maximum number is 69, what is the probability that the number of people who show up will exceed the capacity of the plane?
              1. 0.0223
              2. 0.0044
              3. 0.0050
              4. 0.0006

          7. Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.
            • 15. n = 721, p = .7
              1. 9.89
              2. 16.42
              3. 15.57
              4. 12.30

          8. Use the given values of n and p to find the minimum usual value μ – 2σ and the maximum usual value μ + 2σ.
            • 16. n = 2220, p = 0.595
              1. Minimum: 1288.19; maximum: 1353.61
              2. Minimum: 1297.771; maximum: 1344.029
              3. Minimum: 1274.641; maximum: 1367.159
              4. Minimum: 1367.159; maximum: 1274.641

          9. Solve the problem.
            • 17. The probability is 0.4 that a person shopping at a certain store will spend less than $20. For groups of size 18, find the mean number who spend less than $20.
              1. 7.2
              2. 8.0
              3. 10.8
              4. 12.0

            • 18. According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16.
              1. 1.88
              2. 2.75
              3. 3.52
              4. 1.66

          10. Determine is the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ – 2σ or greater than μ + 2σ.
            • 19. A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual get 554 consumers who recognize the Dull Computer Company name?
              1. Yes
              2. No

          11. Use the Poisson Distribution to find the indicated probability.
            • 20. For a certain type of fabric, the average number of defects in each square foot of fabric is 0.4. Find the probability that a randomly selected square foot of the fabric will contain more than one defect.
              1. 0.7319
              2. 0.0536
              3. 0.9384
              4. 0.0616

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