Normal Distribution with Non-Standard Mean and Variance: Solving for P(X>1)

[ak123456]

Homework Statement

how to do with the normal distribution if the mean is not 0 variance is not 1.
for example p(x>1) if x-N(2,3) ?

Homework Equations

The Attempt at a Solution

 

[Mark44]

You use a transformation of your random variable X, namely z = (x - mu)/sigma. Here z is N(0, 1).
The transformation works the other way, too, with x = z sigma + mu.
The probability you want is
P(x > 1)
= P(z sigma + mu > 1)
Work with the expression in parentheses above, using the properties of inequalities, to get a probability involving z all by itself. The idea is that if you have equivalent inequalities, the probabilities will be equal. You should end up with a probability of the form P(z > ...). You can find that probability in a table of standard normal distribution probabilities.