Question

We want to take a sample of 100 items out of a large batch for quality control purposes. Based on past history, the proportion of defective items is 4%. Can we use the normal approximation to the binomial distribution to find the probability of finding more than 5 defective items in the sample of 100

Answer 1

Answer:

np < 5, so we cannot use the normal approximation to the binomial distribution to find the probability of finding more than 5 defective items in the sample of 100

Step-by-step explanation:

If we have:

np > 5 and n(1-p) > 5

In which p is the proportion and n is the sample size, we can use the normal approximation to the binomial.

In this problem, we have that:

$n = 100, p = 0.04$

np = 100*0.04 = 4 < 5

So we cannot use the normal approximation to the binomial

np < 5, so we cannot use the normal approximation to the binomial distribution to find the probability of finding more than 5 defective items in the sample of 100