Question: 55. A quality control engineer is interested to find how many parts he/she needs to inspect to detect the first defective part. If the probability

55. A quality control engineer is interested to find how many parts he/she needs to inspect to detect the first defective part. If the probability that a randomly selected part is defective is p and X is the number of parts inspected needed to detect the first defective part, then X is a random variable that is distributed by the geometric distribution.

(a) Determine the probability distribution of the random variable X.

(b) Determine the expected value and the variance of X.

(c) Determine P(X = 20), given that p = 0.07.

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