Question

I. A factory produces a type of micro chip with defective rate 0.5%. The chips are packaged as set of 10. Each set is considered as returnable if it contains more than 1 defective chips. (a) (10 points) What is the probability that a randomly chosen set is returnable? (b) (10 points) If a customer buys 10000 sets, approximate the probability that he will return more than 5 sets?

Answer 1

(a)

Let X is a random variable shows the number of defective chips in a set of 10. Here X has binomial distribution with parameters n=10 and p=0.005.

So the probability that a randomly chosen set is returnable is

Answer: 0.0011

(b)

Let Y is a random variable shows the number of set out of 1000 are returnable. Here Y has binomial distribution with parameters n=10000 and p=0.0011.

Using normal approximation, Y has approximately normal distribution with mean and SD as follows:

The z-score for Y = 5+0.5 = 5.5 is

The required probability is:

P(Y > 5) = P(Y> 5.5) = P(z > -1.66) = 0.9515

Answer: 0.9515