A fair sample of a batch of \'memory chips\' have been tested and found that the

Question

A fair sample of a batch of 'memory chips' have been tested and found that the defective percentage is 1%. We randomly buy 7 memory chips from this batch. (Assume that the entire batch has more than 7 memory chips.) a) Which probability distribution describes this experiment? Find the following: b) Probability of exactly 2 of them being defective. c) Probability of at least 2 of them being defective. d) Probability of at most 2 of them being defective. e) Probability of at least 5 of them being non-defective. f Expected number of defective memory chips.

Explanation / Answer

Let X be the number of chips being defective

p=0.01 i.e. defective % and n=7

(a) Binomial distribution describes this experiment with parameters n and p

(b) P(X=2) = 7C2 (0.01)2 (1-0.01)7-2 = 0.002

(c) P(X>=2) = 1-P(X<2)

=1 - P(X=0) - P(X=1)

=1- 7C0 (0.01)0 (0.99)7 - 7C1(0.01)1 (0.99)6

=0.00203

(d)P(X<=2) = P(X=0) + P(X=1) + P(X=2)

Using above parts :

=0.999966

(e) P (non defective >=5) = P(X<=2) = 0.999966

(f) expectation of binomial = np = 7(0.01) = 0.07

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