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# Calculate the mean and standard deviation for a sample from a machine that produces defects 3% of the time.

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A machine that manufactures automobile pistons is estimated to produce a defective piston of the time. Suppose that this estimate is correct and that a random sample of pistons produced by this machine is taken.

a. Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

a. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

##### Solution Summary

The following solution describes the process of finding the mean and standard deviation of defects expected in a sample. A machine is known to produce 3% defects and the sample taken is 80.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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