Paint manufacturer uses a machine to fill 1- gallon cans with paint- they want to estimate the mean volume of paint the machine is putting in the cans within 0.25 of an ounce. determine the minimum sample size needed to construct a 90% confidence interval for the population mean. assume the population standard deviation is 0.85 ounces.

So the answer for this case would be n=32 rounded up to the nearest integer

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

represent the sample standard deviation

n represent the sample size (variable of interest)  

The confidence interval for the mean is given by the following formula:

The margin of error is given by this formula:

   (1)

And on this case we have that ME =0.25 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

  (2)

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05,0,1)", and we got , replacing into formula (2) we got:

So the answer for this case would be n=32 rounded up to the nearest integer