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Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter =40.125millimeters (mm). The machine has some variability, so the standard deviation of the diameters is =0.002mm. The machine operator inspects a random sample of 4 axles each hour for quality control purposes and records the sample mean diameter x-x. Assume the machine is working properly.

a. Identify the mean of the sampling distribution of x-x.

b. Calculate and interpret the standard deviation of the sampling distribution of x-x.

Short Answer

Expert verified

(a). The units of the mean of the sampling distribution of the sample mean are the sample as the units of the population mean and thus the mean is 40.125mm

(b). The sample mean diameter of 4 randomly selected axles in an hour varies on average by 0.001mmfrom the mean diameter of 40.125

Step by step solution

01

part(a) step 1: Given information

The values are

=40.125=0.002n=4
02

part(a) step 2: Calculation

The sample mean's sampling distribution mean is equal.

x==40.125

The sample as the units of the population mean are the units of the mean of the sampling distribution of the sample mean, and so the mean is 40.125mm

03

Part(b) step 1: Given information 

The values are,

=40.125=0.002n=4

Let use the following formula

x=n

04

Part(b) step 2: Calculation

The sample mean is the mean of the sampling distribution.

x==40.125

The standard deviation of the sample mean's sampling distribution is

x=n=0.0024=0.0022=0.001

The units of the sampling distribution's standard deviation of the sample mean are the same as the units of the population standard deviation, so the standard deviation is 0.001mm.

In an hour, the sample mean diameter of four randomly selected axles fluctuates by an average of 0.001mmfrom the mean diameter of 40.125

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