# Probability Distribution, Confidence Interval, Hypothesis

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A vendor supplies refreshments at a baseball stadium and must plan for the possibility of a World Series contest. In the accompanying table, x represents the number of games required to complete a World Series contest. P(x) is the probability that x games are required to complete the contest.

x P(x)

4 0.12

5 0.253

6 0.217

7 0.41

12) What is the average number of games required to complete a contest?

13) What is the standard deviation for the number of games required?

14. In a time-use study, 20 randomly selected managers were found to spend a mean of 2.40 hours per day on paperwork. The standard deviation of the 20 scores was 1.30 hours. Construct a 95% confidence interval for the mean time spent per day on paper work by all managers.

15) The mean time between failures for a Downplunk radio used in light aircraft is 85 hours. After 35 radios were modified, in an attempt to improve reliability, tests showed that the mean time between failures for the sample is 420 hours and the standard deviation is 24 hours. USe a 0.05 significance level to test the claim that the modifications improved reliability.

Use the following information for the next two problems.

Environmental concerns conflict with modern technology, as in the case with birds that pose a hazard to aircraft during takeoff. An environmental group states that incidents of bird strikes are too rare to justify killing the birds. Sample data consist of 74 aborted takeoffs in which the aircraft overran the runway. Among those 74 cases, 5 were due to bird strikes.

16) Find a 95% confidence interval for the proportions of aborted takeoffs due to birds.

17) A pilot group claims that among aborted takeoffs leading to an aircraft's going off the end of the runway, 10% are due to bird strikes. Test the pilot group's claim using alpha= 0.05

18) In one part of a test developed by a psychologist, the test subject is asked to form a word by unscrambling the letters "ciiatttsss." Given below are the times (in seconds) required by 15 randomly selected persons to unscramble the letters. At the alpha = 0.05 level of significance, test the claim that the mean time is equal to 60 seconds. Assume the population is approximately normal.

68.7

27.4

26

60.5

34.6

61.1

68.6

48.4

43.6

39.5

85.3

26.3

43.4

83.7

68.9

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