If commuting times are normally distributed with mean 30 min

If commuting times are normally distributed with mean 30 minutes, and standard deviation is 16 minutes.

What is the probability that a commuting time is shorter than 25 minutes? Calculate by hand

Solution

Normal Distribution
Mean ( u ) =30
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 25) = (25-30)/15
= -5/15= -0.3333
= P ( Z <-0.3333) From Standard Normal Table
= 0.3694