Variable X is normally distributed with a mean of 25 and a s

Variable X is normally distributed with a mean of 25 and a standard deviation of 5. What is the probability of randomly choosing someone with a score of 15 or less ?

Solution

Normal Distribution
Mean ( u ) =25
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 15) = (15-25)/5
= -10/5 = -2
= P ( Z >-2) From Standard Normal Table
= 0.9772                  
P(X < = 15) = (1 - P(X > 15)
= 1 - 0.9772 = 0.0228