assume the random variable x is normally distributed with me

assume the random variable x is normally distributed with mean of 90 and standard deviation of 4. Find the indicated probability. (P 80 <X < 85).

Solution

Normal Distribution
Mean ( u ) =90
Standard Deviation ( sd )=4
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 80) = (80-90)/4
= -10/4 = -2.5
= P ( Z <-2.5) From Standard Normal Table
= 0.00621
P(X < 85) = (85-90)/4
= -5/4 = -1.25
= P ( Z <-1.25) From Standard Normal Table
= 0.10565
P(80 < X < 85) = 0.10565-0.00621 = 0.0994