Question

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 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.

If this was the appropriate answer mark as the brainliest!
-procklown

Answer 2

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 = 45

Sample std error = 0.30/sqrt 45 =0.0447

x bar = 136.9

Create hypotheses as:

H0: sample mean = 137

Ha: sample mean not equal to 137

(Two tailed test)

Test statistic = (136.9-137)/0.0447

=-2.237

p value = 0.0257

Since p >0.01, at 99% level we accept null hypothesis

Machine need not be reset.