SOLUTION: If 40% of the people in the community use the library in one year, for a sample of 4 people find: i) The probability that at least 3 used the library. ii) The mean number of li

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Question 835718: If 40% of the people in the community use the library in one year, for a sample of 4 people find:
i) The probability that at least 3 used the library.
ii) The mean number of library users.
iii) The variance of the number of library users. (
Answer by reviewermath(1029) About Me  (Show Source):
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If 40% of the people in the community use the library in one year, for a sample of 4 people find:
X~Binomial(4, 0.4)
i) The probability that at least 3 used the library.
P(X ≥ 3) = sum%28+%28matrix%282%2C1%2C4%2Cx%29%29%280.4%5Ex%29%280.6%5E%284-x%29%29%2C+x+=+3%2C+4+%29 = highlight%280.1792%29
ii) The mean number of library users.
mean, E(X) = np = 4(0.4) = highlight%281.6%29
iii) The variance of the number of library users
variance, Var(X) = npq = 4(0.4)(0.6) = highlight%280.96%29