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.