A tractor manufacturing company machines axles to extremely small tolerances. The main power axles have a mean diameter of 3.0000 inches and a standard deviation of 0.0050 inch. What is the probability that a given axle will have a diameter between 2.9915 and 3.0004 inches? Assume that errors are normally distributed.

Answer 1

Using the computational tool at
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html ,
I get 48.7%

Answer 2

I need help understanding how to solve by going through step by step. I do not want to know the answer, I need to learn the process. Please help me through that.

Answer 3

You need a table of the normal distribution or "error" function, e^-x^2. This involves an integral that must be calculated "by hand" because there is not simple closed-form integral other than the error function itself. The web site I gave you performs this calculation automatically.

Answer 4

For a step by step explanation, see
http://stattrek.com/Tables/Normal.aspx