Consider a normal random variable X with mean 2 and variance

Consider a normal random variable X with mean 2 and variance 9. What is Pr(0 ? X ? 3)? (Using \"standard normal table\")

Solution

m =2

V = 9

sd = sqrt(V)

sd = 3

z = (x-m)/sd

P(0<=x<=3) = P((0-2)/3 <= z <= (3-2)/3)

P(0<=x<=3) = P( -0.667 <= z <= 0.333)

P(0<=x<=3) = P(z<= 0.333) - P(z<= -0.667)

P(0<=x<=3) = 0.6293 - 0.2514

P(0<=x<=3) = 0.3779