Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.41 ounces and a standard deviation of 0.04 ounce. Find the probability that a randomly selected bottle contains between 12.31 and 12.37 ounces.

Answer 1

Last time I taught this many years ago, we still used tables or charts of "normal distribution values"

We would have to convert everything to z-scores and then look up values.

Here is a little applet that has taken the drudgery away from that
http://www.analyzemath.com/statistics/normal_calculator.html

just enter 12.41 for the mean, .04 for SD, and click on 'between' and enter the values of 12.31 and 12.37
I get .1524

I have used
http://davidmlane.com/hyperstat/z_table.html

in the past, it is really good, and shows the graph, but lately I keep getting an error when I try to enter the SD.
Perhaps it will work for you

Answer 2

Thank you Reiny, your comments are always helpful. I learn everytime with you.