呢條數點計嫁?有冇人可以救我?
2011-10-24 3:54 am
A manufacturing process produces silicon chips, 90% of which are defective. 12 chips are taken at random from a large production run. (a) Find the probability that (i) exactly 5 chips are defective. (ii) at least 3 chips are defective.(b) What are the mean and standard deviation of the probability distribution?
回答 (1)
2011-10-24 4:14 pm
✔ 最佳答案
This is a binomial dist. with n = 12 and p = 90% = 0.9(ai) P(Exactly 5 defective) = (12C5)(0.9^5)(1 - 0.9)^7
(aii) P(At least 3 defective) = 1 - P(No defective) - P(1 defective) - P(2 defective)
= 1 - (12C0)(1 - 0.9)^12 - (12C1)(0.9)(1 - 0.9)^11 - (12C2)(0.9^2)( 1 - 0.9)^10
(b) Mean = np = 12 x 0.9 = 10.8
s.d. = sqrt nqp = sqrt (10.8 x 0.1) = sqrt 1.08 = 1.03923
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