(10.2)
n = 150, p = 0.09, q = 1 - p = 0.91
P(x) = C(n, x) p^x q^(n - x)
(a) Probability distribution of x is a binomial distribution
(b) Mean = np = 150 * 0.09 = 13.5 and Standard deviation = √(npq) = √(150 * 0.09 * 0.91) = 3.505
(c) P(15) = C(150, 15) 0.09^15 0.91^(150 - 15) = 0.099
(d) P(x ≤ 10) = P(0) + P(1) + P(2) + ... + P(10)
= C(150, 0) 0.09^0 0.91^(150 - 0) + C(150, 1) 0.09^1 0.91^(150 - 1) + ... + C(150, 10) 0.09^10 0.91^(150 - 10)
= 0.2
(e) P(x > 25) = 1 - P(x ≤ 25)
= 1 - [C(150, 0) 0.09^0 0.91^(150 - 0) + C(150, 1) 0.09^1 0.91^(150 - 1) + ... + C(150, 25) 0.09^25 0.91^(150 - 25)]
= 0.00091
Please hata persu is audited more than twice. 102, According to The world Bank, only 9%...
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