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  3. 6. suppose that you choose a student at random, an

6. Suppose that you choose a student at random, and let the random variable “H” represent...

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Statistics

6. Suppose that you choose a student at random,and let the random variable “H” represent the student’s studyingtime (in hours) last week. Suppose that “H” has a uniformdistribution on the interval (25, 35). If you randomly select 10students and that each person’s studying time follows this sameprobability distribution, independently from person to person,determine the probability that at least two of the students studiedfor more than 32 hours last week.  

Answer & Explanation Solved by verified expert
4.4 Ratings (710 Votes)

X ~ U (25 , 35)

P(one student studies more than 32 hours) = P(X > 32)

                                                                     = (35 - 32) / (35 - 25)

                                                                     = 0.3

p = 0.3

n = 10

This is a binomial distribution

P(X = x) = 10Cx * 0.3x * (1 - 0.3)10-x

P(X > 2) = 1 - (P(X = 0) + P(X = 1))

              = 1 - (10C0 * 0.30 * 0.710 + 10C1 * 0.31 * 0.79)

              = 1 - 0.1493

              = 0.8507
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