A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 137 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 136.9 ounces. Does the machine need to be reset? Explain your reasoning.

Question

Mathematics

Madelynn Moyer

24 February, 08:55

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 137 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 136.9 ounces. Does the machine need to be reset? Explain your reasoning.

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Answers (1)

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Evangeline Castaneda · Answer 1

Standard error of mean = Sigma / sqrt n

= 0.30 / sqrt 45

= 0.30 / 6.71

= 0.045

Xbar - Mu = 138.9 - 139 = - 0.1

- 0.1 / 0.045 = - 2.22

YES, because the sample mean lies beyond 2 Standard deviations on the left side of mu.

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