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# A quality engineer takes a random sample of 100 steel rods

ISBN: 9780073401331 38

## Solution for problem 10E Chapter 4.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 10E

A quality engineer takes a random sample of 100 steel rods from a day's production, and finds that 92 of them meet specifications.

a. Estimate the proportion of that day's production that meets specifications, and find the uncertainty in the estimate.

b. Estimate the number of rods that must be sampled to reduce the uncertainty to 1%.

Step-by-Step Solution:

Answer :

Step 1 of 3 :

Given, a random sample of 100 steel rods is taken by the engineer and he finds that 92 of the 100 samples are meet specification.

The goal of the problem is

We have to find the proportion of that day’s production that meets specifications, and find the uncertainty in the estimate.We have to estimate the number of rods that must be sampled to reduce the uncertainty to 1%

Step 2 of 3 :

We have the total sample size is 100

Proportion =

=

=

= 0.92

Therefore, the proportion is 0.92

The uncertainty of the estimate is

then ,  =

=

=

= 0.02713

Hence, the uncertainty of the estimate is    = 0.02713

Step 3 of 3

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A quality engineer takes a random sample of 100 steel rods