pants) herns produced on an assembly line meet the dimensional tolerances 95% of

Question

pants) herns produced on an assembly line meet the dimensional tolerances 95% of the time and each trial is independent. 4l lfeight inems are sampled, what is the probability that all meet tolerances? What is the probability that at least seven meet the tolerances? number of samples needed until an item does not meet tolerance? What is the standard deviation of the number of trials needed until the first such item is detected? 4.2 Sampling is performed until an item does not meet tolerance. What is the mean

Explanation / Answer

Question 4

here sample size n = 8

probability of success = 0.95

4.1 Pr(All meet tolerances) = 0.958 = 0.6634

Pr(at least 7 meet the tolerances = Pr(7 meet tolerances) + Pr(all 8 meet tolerances)

= 8C7 (0.95)7 * (0.05)1  + 8C8 (0.95)8

= 0.2793 + 0.6634 = 0.9427

4.2

Here if x is the number of samples needed untile an item does not meet tolerance.

probability of an item does not meet tolerance = 0.05

so the distribution here geometric here

f(x) = (0.95)x-1 0.05

E[X] = 1/0.05 = 20

Variance = (1-p)/p2 = (1 - 0.05)/0.052 = 380

Standard deviation = sqrt(380) = 19.49

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