Statistics Question

Question

A potential buyer will sample videotapes from a large lot of new video tapes to check for defective tapes. If five percent of the lot is defective and she takes a random sample of 80 tapes, what is the probability that she will find at least 7 defective tapes?

Answer 1

x = number of defective tapes is a binomial variable, so we can use binomial formula for computing probability that x will take on a certain number.

probability that k out of n tapes are defective:

P(x = k) is 80! (0.05)^k (0.95)^(n-k)

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k! (n-k)!

The probability that at least 7 are defective is the same as 1 - the probability that less than 7 are defective.

Compute P(x=k) for k = 0, 1, 2, 3, 4, 5 and 6, sum the probabilities, then subtract that value from 1.