X is a normally distributed random variable with mean 0 and

X is a normally distributed random variable with mean 0 and standard deviation 0.75. Find the probability indicated.

P(4.02 < X < 3.82)

P(X > 4.11)

Solution

a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -4.02) = (-4.02-0)/0.75
= -4.02/0.75 = -5.36
= P ( Z <-5.36) From Standard Normal Table
= 0
P(X < 3.82) = (3.82-0)/0.75
= 3.82/0.75 = 5.0933
= P ( Z <5.0933) From Standard Normal Table
= 1
P(-4.02 < X < 3.82) = 1-0 = 1                  
b)
P(X > 4.11) = (4.11-0)/0.75
= 4.11/0.75 = 5.48
= P ( Z >5.48) From Standard Normal Table
= 0