Question

Suppose a lot of 10,000 items has 200 defective items and that a random sample of 30 is drawn from the lot. What is the binomial approximation (to five decimal places) of the probability of getting exactly 2 defective items in the sample?

Answer 1

Let , 'p' be the probability of the item is defective.

Here , p=200/10000=0.02

Let , X be the number of defective items.

Here , X has binomial distribution with parameter n=30and p=0.02

Therefore , teh PMF of X is ,

; x=0,1,2,.....,n and q=1-p

= 0 ; otherwise

Now ,

Therefore , the probability of getting exactly 2 defective items in the sample is 0.09883