Question 8.

A machine fills cans of Coca Cola. The amount of cola that ends up in cans is a random variable with a mean of 11.9 ounces and a standard deviation of 0.1 ounces.

• There are supposed to be 12 ounces in each can. What percentage of cans will be under filled?
• Suppose I can change the mean from 11.9 to any value I want. What value should I set the mean to in order that 1% of the cans are under filled?
• Suppose the mean must stay at 11.9, but I can adjust the standard deviation . What value of will result in 1% of the cans being under filled?
• Suppose Coca Cola decides that a can is acceptable if it contains between 11.8 and 12.2 ounces of cola. Given the N(11.9,0.01) distribution we've been assuming, what is the probability that a given can is acceptable?
• Suppose quality control decides to inspect 10 cans. What is the probability that all 10 cans are acceptable by the same standards as in d)?
• What is the probability that quality control finds more than 15 unacceptable cans if they randomly select 100 cans?