Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 131131 millimeters, and a standard deviation of 88 millimeters.If a random sample of 5050 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 33 millimeters? Round your answer to four decimal places.

Question
Asked Nov 6, 2019

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 131131 millimeters, and a standard deviation of 88 millimeters.

If a random sample of 5050 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 33 millimeters? Round your answer to four decimal places.

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Expert Answer

Step 1

First let the given quantities are

 

Mean diameter (m) = 131131 mm

Standard deviation (σ) = 88 mm

Sample size n = 5050


X - m = 33 mm

 

standard deviation of sample mean = standard deviation/n = 88/5050 = 0.0174

 

probability that the sample mean would differ from the population mean by greater than 33 millimetres that means is vary by 33 so it can be less than mean - 33 or greater than mean + 33.

 

For probability, we need to find the z- scor...

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