Question

A manufacturing firm produces a product that has a ceramic coating. The coating is baked on to the​ product, and the baking process is known to produce 10​% defective items. Every​ hour, 25 products from the thousands that are baked hourly are sampled from the​ ceramic-coating process and inspected. Complete parts a through c.

a. What is the probability that 5 defective items will be found in the next time sample of 25?

The probability is ________ that 5 defective items will be found in the next sample of 25? (round to 4 decimal places as needed)

b. On average, how many defective items would be expected to occur in each sample of 25?

Each sample of 25 would be expected to have ______ defective item(s). (type an integer or decimal)

c. How likely is it that 20 or more non defective (good) items would occur in a sample due to chance alone?

The probability that 20 or more non defective (good) items would occur in a sample due to chance alone is approximately _______. (round to four decimal places as needed)

Answer 1

Let X denote the number of defective items in a sample. Then,

a)

Required probability =

b)

We know that expected value for a Binomial distribution is given by:

which is the expected number of defective items in each sample.

c)

Required probability = P(20 or more non-defective) = P(5 or less defective)