At Jen and Perry Ice Cream Company, the machine that fills one-pound cartons of Top Flavor ice

Question:

At Jen and Perry Ice Cream Company, the machine that fills one-pound cartons of Top Flavor ice cream is set to dispense 16 ounces of ice cream into every carton. However, some cartons contain slightly less than and some contain slightly more than 16 ounces of ice cream. The amounts of ice cream in all such cartons have a normal with a mean of 16 ounces and a standard deviation of .18 ounce.
a. Find the probability that the mean amount of ice cream in a random sample of 16 such cartons will be
i. Between 15.90 and 15.95 ounces
ii. Less than 15.95 ounces
iii. More than 15.97 ounces
b. What is the probability that the mean amount of ice cream in a random sample of 16 such cartons will be within .10 ounce of the population mean?
c. What is the probability that the mean amount of ice cream in a random sample of 16 such cartons will be less than the population mean by .135 ounce or more? Distribution
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