# Chapter 6 Lessons 1 and 2

### Walter White's Math Lesson

## Graphs of Normal Probability Distributions Lesson 1

*Gaussian*.

## Application

A rather complicated formula, presented later in this section, defines a normal distribution in terms of *m* and *s*, the mean and standard deviation of the population distribution.

## Bell Shape Curve

We see that a general normal curve is smooth and symmetrical about the vertical line extending upward from the mean *m*.

Notice that the highest point of the curve occurs over *m*. If the distribution were graphed on a piece of sheet metal, cut out, and placed on a knife edge, the balance point would be at *m*.

## Properties of a Normal Curve

2. The curve is symmetrical about a vertical line through

## Empirical Rule

1 standard deviation=68%

2 standard deviation=95%

3 standard deviation=99.7%

## Solution to Problems

Since *m* = 600 and *m* + *s* = 600 + 100 = 700, we see that the shaded area is simply the area between *m* and *m* + *s*.

The area from *m* to *m* + *s* is 34% of the total area.

This tells us that the probability a Sunshine radio will last between 600 and 700 playing hours is about 0.34.