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Find the required probability for binomial distribution.
Binomial Probabilities: Multiple-Choice Quiz Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has 5 answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 10 question, find the indicated probabilities.
a) What is the probability that he will answer all questions correctly?
b) What is the probability that he will answer all questions incorrectly?
c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in Table 3 of appendix II. Then use the fact that P(r > 1) = 1 - P(r = 0). Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?
d) What is the probability that Richard will answer at least half the questions correctly?
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Last week Sarah had exams in Math and in Spanish. On the Math exam, the mean was u, = 30 with a = 5, and Sarah had a score of X - 45. On the Spanish exam, the mean was u, = 60 with 0 = 6 and Sarah had a score of X = 65. For which class must Sarah ..
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