A machine used to fill gallon sized paint cans is regulated so the amount of pai

Question

A machine used to fill gallon sized paint cans is regulated so the amount of paint dispensed has a mean of 130 oz and standard deviation of 0.40 oz. you randomly select 45 cans and measure the contents. The sample means of cans is 129.9 oz. does the machine need to be reset? Explain why or why not. A machine used to fill gallon sized paint cans is regulated so the amount of paint dispensed has a mean of 130 oz and standard deviation of 0.40 oz. you randomly select 45 cans and measure the contents. The sample means of cans is 129.9 oz. does the machine need to be reset? Explain why or why not.

Explanation / Answer

Solution:- Standard error of mean = Sigma / sqrt n
= 0.40/sqrt 45
= 0.0596
Xbar - Mu = 129.9 - 130 = -0.1

= -0.1/0.0596 = -1.6778 = -2(rounded)
YES, because the sample mean lies beyond 2 Standard deviations on the left side of mu

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