Using the binomial distribution formula, the probability that the box of 250 contains at least 5 defectives is approximately 0.001.
How the binomial distribution probability is computed:
The probability of a component being defective = 0.008 (8/1,000)
The number of components in each box = 250.
The binomial distribution formula:
P(X≥5)=1−P(X<5)
where the number of defective components in a box = X
Calculating P(X < 5) using the cumulative distribution function (CDF) of the binomial distribution in a calculator:
P(X<5) ≈ 0.999
P(X≥5) = 1−P(X<5) ≈ 0.001
Thus, the probability that the box contains at least 5 defectives is approximately 0.001.