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.
(a) If the claim is true, then X~ Bin Bin(1000, 0.05), so X is approximately normal with mean 
=1000(0.05)=50 and 
To find P (X ? 75), use the continuity correction and find the z-score of 74.5.
The z-score of 74.5 is (74.5-50)/6.89202=3.55
The area to the right of z= 3.55 is 1 ? 0.9998 = 0.0002.
P (X ? 75)=0.0002.
(b) Yes. Only about 2 in 10,000 samples of size 1000 will have 75 or more nonconforming tiles if the goal has been
reached.
(c) No, because 75 nonconforming tiles in a sample of 1000 is an unusually large number if the goal has been
reached.
(d) If the claim is true, then X ? Bin(1000, 0.05), so X is approximately normal with mean =1000(0.05)=50 and
To find P(X ? 53), use the continuity correction and find the z-score of 52.5.
The z-score of 52.5 is (52.5 ? 50) ? 6.89202 = 0.36
The area to the right of z= 0.36 is 1 ? 0.6406 = 0.3594.
P(X ? 53)=0.3594.
(e) No. More than 1/3 of the samples of size 1000 will have 53 or more nonconforming tiles if the goal has been reached.
(f) Yes, because 53 nonconforming tiles in a sample of 1000 is not an unusually large number if the goal has been reached.
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