Question 1051583
We use the binary probability distribution
:
The probability of non-defective items is 1 - 0.25 = 0.75
:
Probability(k items are non-defective) = nCk * p^k * q^(n-k), where n is number of items produced, k = number of non-defective items, p = probability of non-defective items, q = 1-p, nCk of the combination of n items taken k at a time
:
a) Probability(k items are non-defective) = nCk * (0.75)^k * (0.25)^(n-k)
:
b) Probability(at least 50 items are produced out of 100) is the summation of
the probabilities for 50, 51, 52, ..., 100
:
Probability(at least 50 items are produced out of 100) = 0.999999