Problem 17E

A new process has been designed to make ceramic tiles. The goal is to have no more than 5% of the tiles be nonconforming due to surface defects. A random sample of 1000 tiles is inspected. Let X be the number of nonconforming tiles in the sample.

a. If 5% of the tiles produced are nonconforming, what is P(X ≥ 75)?

b. Based on the answer to part (a), if 5% of the tiles are nonconforming, is 75 nonconforming tiles out of 1000 an unusually large number?

c. If 75 of the sample tiles were nonconforming, would it be plausible that the goal had been reached? Explain.

d. If 5% of the tiles produced are nonconforming, what is P(X ≥ 53)?

e. Based on the answer to part (d), if 5% of the tiles are nonconforming, is 53 nonconforming tiles out of 1000 an unusually large number?

f. If 53 of the sample tiles were nonconforming, would it be plausible that the goal had been reached? Explain.

Solution

Step 1 of 7

Here the goal is to have no more than 5% of the tiles nonconforming

So p=0.05

Here the sample size 1000

n=1000

Let X is the no.of non conforming tiles

Here XB(1000,0.05)

Now X is approximately normal with

Mean =1000(0.05)

= 50

Standard deviation =

=

=6.89