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A new process has been designed to make ceramic tiles. The
Chapter 4, Problem 17E(choose chapter or problem)
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 \(P(X\geq75)\)?
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 \(P(X\geq53)\)?
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.
Equation Transcription:
Text Transcription:
P(X{>/=}75)
P(X{>/=}53)
Questions & Answers
QUESTION:
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 \(P(X\geq75)\)?
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 \(P(X\geq53)\)?
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.
Equation Transcription:
Text Transcription:
P(X{>/=}75)
P(X{>/=}53)
ANSWER:
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