Problem 1: The weights of newborn elephants are normally distributed with a mean of 225 pounds and a standard deviation of 45 pounds.

Required:

a) Find the probability that a newborn elephant weighs between 250 and 275 pounds. You must show your work using a calculator function to receive credit.

b) Find the probability that a newborn elephant weighs more than 210 pounds. You must show your work using a calculator function to receive credit.

c) A zoo carefully monitors any newborn elephants born at their park. If a newborn elephant's weight falls in the bottom 5%, then the zoo takes special measures to ensure the health of the "little" guy or gal. Find the birth weight below which the zoo takes these precautions. Round your answer to the nearest pound. You must show your work using a calculator function to receive credit.

Problem 2: People counting calories have to be careful about the estimates placed on prepackaged food. Suppose testing shows that a certain brand of doughnut has a mean calorie count of 240, so that is the amount printed on the package. However, testing shows that the calories counts vary, following a normal distribution with a standard deviation of 15 calories.

Required:

a) Find the probability that an individual doughnut for this brand contains more than 275 calories. You must show your work using a calculator function to receive credit.

b) Find the probability that a random sample of 12 of these doughnuts contains a mean number of calories between 230 and 260. You must show your work using a calculator function to receive credit.

3. A brewery filling machine is adjusted to fill quart bottles with a mean of 32 oz of ale and a standard deviation of 0.12 oz of ale. Find the probability that a randomly selected sample of 36 bottles has a mean fill amount which is less than 31.95 oz of ale. You must show your work using a calculator function to receive credit.