A machine used to fill gallon-sized paint cans is regulated so that the amount o

Question

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 127 ounces and a standard deviation of 0.40 ounce. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 126.9 ounces. Does the machine need to be reset? Explain your reasoning.

(Yes/No), it is (Very Unlikely/Likely) that you would have randomly sampled 45 cans with a mean equal to 126.9 ounces, because it (Does not Lie/Lies) within the range of a usual event, namely within (1/2/3 Standard Deviations) of the mean of the sample means.

Explanation / Answer

No, It is very unlikely that you would have randomly sampled 45 cans with a mean equal to 126.9 ounces, because it lies within the range of an usual event, namely within 1 standard deviation of the mean of the sample means.

That is mu+/-sigma

=(127-0.40,127+0.40)

=(126.6,127.4)

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