A normal distribution has a mean of 10 and standard deviatio

A normal distribution has a mean of 10 and standard deviation 2. Find the value of the 20th percentile.

Solution

The exact Z value holding 20% of the values below it is -0.84162 which was determined from the table of standard noramal probabilities.

Using Z=-0.84162, the 20th percentile of normal distribution of mean (x_) of 10 and standard deviation (s) 2 is

=x_+Zs=10-0.84162*2=8.3168.