A beverage company uses a machine to fill half-gallon bottles with fruit juice (see figure). The company wants to estimate the mean volume of water the machine is putting in the bottles within 0.25 fluid ounce.

(a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 1 fluid ounce.

(b) The sample mean is exactly 64 fluid ounces. With a sample size of 68, a 95% level of confidence, and a population standard deviation of 1 fluid ounce, does it seem possible that the population mean could be greater than 63.85 fluid ounces? Explain.

Transcribed Image Text:

Error tolerance = 0.25 fl oz Talley Gro Orange Juice ite Pule 64 fl oz Volume = 1/2 gal (64 fl oz)