Unformatted text preview: 4. A fair coin is tossed two times, and the events A and B are deﬁned as follows: A: { At least one head is observed } B: { The number of heads observed is odd } (a) Write the sample space. (b) Are A and B independent? (c) Calculate P ( B  A ) . 5. A soccer team has probability of 0.4 of wining any particular game. In a season, it plays 7 conference games. (a) Using binomial distribution, identify n and p . (b) Find the probability that the team wins 4 of its conference games. 6. The mean lifetime of a sample of 100 ﬂorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If μ is the mean lifetime of all bulbs produced by the company, test the hypothesis μ = 1600 hours against the alternative hypothesis μ < 1600 hours , using a level of signiﬁcance 0 . 05 . Find the P value of the test....
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 Spring '08
 TA
 Statistics, Probability theory, average score, conference games

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