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.

Answer:Step-by-step explanation:Let X be the amount of paint dispensed by a machine used to fill gallon=sized paint cans.X is Normal(137, 0.30)Sample size = 45Sample std error = 0.30/sqrt 45 =0.0447x bar = 136.9Create hypotheses as:H0: sample mean = 137Ha: sample mean not equal to 137(Two tailed test)Test statistic = (136.9-137)/0.0447=-2.237p value = 0.0257Since p >0.01, at 99% level we accept null hypothesisMachine need not be reset.