Suppose that the weight of tomato juice in mechanically filled cans follows a normal distribution with a mean ƒÝ of 464 grams and a standard deviation ƒã of 8 grams. What proportion of cans contain between 454 and 474 grams of tomato juice?

Answer 1

the beauty of this applet is that you can enter the data values as is, without changing them to z-scores.

http://davidmlane.com/hyperstat/z_table.html

Since these kind of questions require the use of tables anyway, I don't see the harm of using the above program directly.