find Pr[63.04=X=70.96]

Question

Given a normal random X with mean 64 and a standard deviation 3, find Pr[63.04≤X≤70.96]

Answer 1

First find the number of standard deviations at either end of the range:

(63.04-64)/3=-.32

(70.96-64)/3=2.32

 

Then find the equivalent probabilities (I use normsdist in Excel):

normsdist(-.32,1)=.3744

normsidst(2.32,1)=.9898

Then P(X<=70.96)-P(X<=63.04)=P(63.04<=X<=70.96)=.615

 

Hope that helps,

Deanna