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A quality control procedure at a manufacturing plant involves randomly selecting five items and accepting a whole lot of at least four of the five items are in perfect condition. From past experiences 59.049% of whole lots are perfect. What is the probability that the next lot will be excepted?

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Answer:

0.32072

Explanation:

Given that :

Number of items selected, n = 5

P(x ≥ 4)

Using binomial relation :

P(x =x) = nCx * p^x * (1 - p)^(n - r)

p = 0.59049 ; 1 - p = 0.40951

P(x ≥ 4) = P(4) + P(5)

P(x = 4) = 5C4 * 0.59049^4 * 0.40951^1 = 0.24893

P(x = 5) = 5C5 * 0.59049^5 * 0.40951^0 = 0.07179

P(x ≥ 4) = P(4) + P(5)

P(x ≥ 4) = (0.24893 + 0.07179) = 0.32072

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