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Question

the probability that a certian part is defective is 0,10. assume that the binominal distribution is applicable and that 25 parts are randomly selected from a very large lot. show all calculations correct to 3 decimal places.

4.1 what is the probibility that exactly two are defective?

4.2 what is the probibility that five or more are defective?

4.3 what is the expected number of defectives in the sample of 25?

Answer 1

n=25

p=0.1

4.1  p(k=2)  =(25 over 2) *  (0.1)^2 * (0.9)^23

= 25*12 * (0.1)^2 * (0.9)^23

4.2  p(k= >5) = 1 - [ p(k=0) + p(k=1) + ... + p(k=5) ]

4.3  E(x) = n * p = 25 * 0.1 = 2.5