Let X be a normal variable with mean 10 and standard deviation of 5. What is
P(0<x<20)?

Hi!!


First of all you must normalize the variable X:

Z = (X-Mu)/STD = (X-10)/5

If X = 0 ==> Z = -2

If X = 20 ==> Z = 2

P(0<X<20) = P(-2<Z<2) for a standard normal random variable Z.

Now follows the use of a table like this:
"Normal Distribution Table"
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html


We find for a = 2.00 that P(0<Z<2) = 0.4772

Due the symmetry of the normal distribution from the mean (remember
that we are using a standard normal random variable - Mu = 0 -) wehave
that:
P(-2<Z<0) = P(0<Z<2) = 0.4772

Then:
P(0<X<20) = P(-2<Z<2) = 
          = P(-2<Z<0) + P(0<Z<2) 
          = 0.4772 + 0.4772 =
          = 0.9544


I hope that this helps you.
Feel free to request for a clarification if it needed.


Regards.
livioflores-ga