Juice Dispensing Machine 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 likely that the population mean could be greater
than 63.85 fluid ounces? Explain.