I am Nirmal. I am student. I have a query which my teacher gave to me as a assignment.The question is on probability and is as follows.

A manufacturer of cotton pins knows that 5% of his products are defective. If he sells cotton pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will have the guaranteed quantity?



I expect tat you are to assume that the distribution of defective pins X is a binomial distribution with n = 100
and p = 0.05 where p is the probability that a pin is defective. Thus X has approximately a normal distribution with

mean = n p = 5 and
variance = n p (n-p) = 100 0.05 (0.95) = 4.75

Now use your knowledge of the normal distribution to find P(X ≤ 10).