The random variable X has a normal distribution with u3 and

The random variable X has a normal distribution with u=3 and sigma =5

Find these probabilities:

P(X <_ -4)

P(X >_ 13)

P( -9 <_ X _< 10)

Solution

Convert x into z score for all then use std normal distribution table for finding prob

The above table shows the conversion of x into z

1) P(X<-4) = P(Z<-1.4) = 0.0808

2) P(Z>-3.2) = 0.5+0.5 = 1.00

3) P(-2.4<Z<-2.6) = 0.4953-0.4918 = 0.0035