Question

An electronics company manufactured a specific component for a tuner amplifier. If found that out of every 1000 component produced, 8 are defective. If the components are parked in boxes of 250. Find the probability that the box contains at least 5 defectives

Answer 1

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.