An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. Suppose that you select a sample of 25 oranges.
a. What is the probability that the sample mean amount of juice will be at least 4.60 ounces?
b. The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?
c. The probability is 77% that the sample mean amount of juice will be greater than what value? Discuss in detail.