Question

It costs more to produce defective items - since they must be scrapped or reworked - than it does to produce non-defective items. This simple fact suggests that manufacturers should ensure the quality of their products by perfecting their production processes instead of depending on inspection of finished products (Deming, 1986). In order to better understand a particular metal stamping process, a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours.(Give answer to nearest whole number.)a) How many parts should be sampled in order to estimate the population mean to within .1 millimeter (mm) with 90% confidence? Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about 2mm.

Answer 1

1,082

Explanation:

The sample size n in Simple Random Sampling is given by

`\bf n=(z^2s^2)/(e^2)`

where

z = 1.645 is the critical value for a 90% confidence level (*)

s = 2 is the estimated population standard deviation

e = 0.1 mm points is the margin of error

so

`\bf n=(z^2s^2)/(e^2)=((1.645)^2(2)^2)/((0.1)^2)=1,082.22\approx 1,083`

rounded up to the nearest integer.

So the manufacturer should test 1,083 parts.

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(*)This is a point z such that the area under the Normal curve N(0,1) outside the interval [-z, z] equals 10% = 0.1

It can be obtained in Excel with

NORMINV(1-0.05,0,1)

and in OpenOffice Calc with

NORMINV(1-0.05;0;1)