Suppose that the number of ounces of soda put into a soft-drink can is normally distributed with µ = 12.05 ounces and σ = 0.03 ounce.
a. Legally, a can must contain at least 12 ounces of soda. What fraction of cans will contain at least 12 ounces of soda?
b. What fraction of cans will contain less than 11.9 ounces of soda?
c. What fraction of cans will contain between 12 and 12.08 ounces of soda?
d. One percent of all cans will weigh more than what value?
e. Ten percent of all cans will weigh less than what value?
f. The soft-drink company controls the mean weight in a can by setting a timer. For what mean should the timer be set so that only 1 in 1000 cans will be underweight?
g. Every day the company produces 10,000 cans. The government inspects 10 randomly chosen cans each day. If at least two are underweight, the company is fined $10,000. Given that µ = 12.05 ounces and σ = 0.03 ounce, what is the probability that the company will be fined on a given day?