2022 VJC P2 Q9
In each batch of manufactured articles, $5\%$ of the articles are found to be defective. A quality inspection is carried out by checking samples of $20$ articles.
(i)
If $2$ or fewer defective articles are found in the sample of $20$, the batch is accepted. Find the probability that the batch is accepted.
[1]
(ii)
Find the least value of $n$ such that the probability of having less than $n$ defective articles in a sample of $20$ articles is greater than $0.99$.
[2]
(iii)
Fifty random samples of $20$ articles each were taken. Find the probability that the average number of defective articles per sample is at most $1.25$.
[3]
(iv)
It is proposed that a smaller sample be taken for inspection. Find the largest value of $k$ such that the probability of having at least $1$ defective article in a sample of $k$ articles is to be less than $0.4$?
[3]
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