Problems

1. Suppose we can set the mean number of ounces of soda that is put into a can. The actual number of ounces has a standard deviation of 0.05 ounces.

   • If we set the mean at 12.03 ounces, and a soda can is acceptable if it contains at least 12 ounces, what fraction of cans is acceptable?

   • What fraction of cans have less than 12.1 ounces?

   • What should we set the mean to if we want, at most, 1 percent of our cans to contain, at most, 12 ounces? Hint: Use the Goal Seek command.

2. Annual demand for a drug is normally distributed with a mean of 40,000 units and a standard deviation of 10,000 units.

   • What is the probability that annual demand is from 35,000 through 49,000 units?

   • If we want to have only a 5 percent chance of running out of the drug, at what level should we set annual production?

3. The probability of winning a game of craps is 0.493. If I play 10,000 games of craps and bet the same amount on each game, what is the probability that I’m ahead? Begin by determining the mean and standard deviation of the profit on one game of craps. Then use the Central Limit Theorem.

4. Weekly sales of Volvo’s Cross Country station wagons are normally distributed with a mean of 1000 and standard deviation of 250.

   • What is the probability that, during a week, from 400 through 1100 station wagons are sold?

   • There is a 1 percent chance that fewer than what number of station wagons are sold during a week?