Wednesday, February 19, 2014
The Normal Distribution

1.  Motivation and Definition of the Normal Distribution
2.  Empirical Rule Revisited
3.  Worksheet on Normal Distribution Calculations
4.  The Standard Normal Distribution --- Then and Now
5.  The Blueprint Principle
6.  Assessing Whether a data set is Normal

Class Problem --- Suppose the heights of the individuals in a certain
population follow a normal distribution.  Furthermore, suppose the middle 80%
of this distribution is comprised of individuals between 155 cm and 195 cm.
Find the mean and standard deviation for this normal distribution.

Challenge Problem --- The last time I bought nylon camping rope, the label on
the rope said something like this:

This rope is rated at 500 lb strength. However, if life and limb

are at stake, do not exceed 100 lb load.

Qualitatively, this makes good sense --- if your life depends on the strength of this
rope, you want to be very confident the rope will not break. But quantitatively, how
were these numbers derived? Suppose the numbers come from controlled lab studies
in which only 10% of ropes of this brand broke when a 500 pound load was applied,
but only 5 out of 1000 ropes broke when subjected to a 100 pound load. If the breaking
strength of this brand of rope is normally distributed, find its mean mu and standard
deviation sigma.