Question

Suppose that the travel time from your home to your office is normally distributed
with a mean of 40 minutes and standard deviation of 7 minutes. If you want to be
95% certain that you will not be late for an office appointment at 1:00pm, what is the
latest time that you should leave home?

Answer 1

From a normal distribution table (example
http://www.math.unb.ca/~knight/utility/NormTble.htm
)
look up the z-value for 95% probability, which is 1.645.

μ=40 minutes, σ=7 minutes.
Calculate n from the transformation of x to z as follows:
z=(x-μ)/σ
x=σz+μ
Everything on the right hand side is know, so calculate x required.

Answer 2

92.9