1. Normal Distribution Problems

2. The fill volume of an automatic filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce.
What is the probability that a randomly chosen can will contain more than 12.5 ounces?
2.5% of the cans will contain less than ______ ounces.

3. The fill volume of an automatic filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce.
If all cans less than 12.2 ounces and more than 12.6 ounces are scrapped, what proportion of cans are scrapped?
Determine the specifications that are symmetric about the mean that include 99% of the can.

4. The mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.1 ounce.
At what value should the mean be set so that 97.5% of all cans exceed 12.0 ounces?
At what value should the mean be set so that 97.5% of all cans exceed 12.0 ounces if the standard deviation can be reduced to 0.05 ounces?

5. The length of an injected-molded plastic case that hold magnetic tape is normally distributed with a mean length of mm and standard deviation of 0.10 mm.
What is the probability that a randomly chosen case will measure more than mm?
What should the process mean be set at to obtain the greatest number of parts between 89.7 and 90.3?

6. The army reports that the distribution of head circumferences among male solders is approximately normal with a mean of 22.8 inches and standard deviation of 1.1 inch.
The army plans to make helmets in advance to fit the middle 98% of head circumferences for male solders.
What head circumferences are small enough or big enough to require custom fitting?

7. The distribution of head circumferences among female solders is approximately normal with mean 22.2 inches and standard deviation 1.4 inches.
Female solders use the same type of helmet as male solders. What percent of solders can be fitted with a made-in-advance helmet?