# MATHEMATICS

1.  Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has five 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 alleight questions, find the indicated probabilities. (Round your answers to three decimal places.)
(a) What is the probability that he will answer all questions correctly?

(d) What is the probability that Richard will answer at least half the questions correctly?

(e) more than 17 out of the next 20 business days

•  Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 47% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.
(a) Out of six adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(b) Compare P(3 or more successes), where p = 0.30, with P(2 or fewer successes), where p = 0.70.

(c) Find the value of P(4 successes), where p = 0.30. (Round your answer to three decimal places.)
P(4 successes) =

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