6. Suppose that you choose a student at random, and let the random variable â€œHâ€ represent...

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6. Suppose that you choose a student at random,and let the random variable â€œHâ€ represent the studentâ€™s studyingtime (in hours) last week. Suppose that â€œHâ€ has a uniformdistribution on the interval (25, 35). If you randomly select 10students and that each personâ€™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.Â Â

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4.4 Ratings (710 Votes)

X ~ U (25 , 35)

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

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.3

p = 0.3

n = 10

This is a binomial distribution

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

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

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

Â Â Â Â Â Â Â Â Â Â Â Â Â = 1 - 0.1493

Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.8507

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6. Suppose that you choose a student at random, and let the random variable â€œHâ€ represent...