Assume X is normally distributed with a mean of 5 and a stan

Assume X is normally distributed with a mean of 5 and a standard deviation of 2. Determine the value for x that solves each of the following. Round the answers to 2 decimal places.

a.) P(X>x)=.5
b.) P(X>x)=.95
c.) P(x<X<5)=.2
d.)P(-x<X-5<x)=.95

Solution

the distribtion is Gaussian or Normal

p(x ) =[1/sqrt(2pisigma^2)]exp[-(x-m)^2/2sig^2...

m = mean sigma = standard deviation

P[a<x<b] = int a to b p(x)dx

there is no closed form solution . you must look up ans in tables

The first one is easy x= 5 since 1/2 on each sided of mean