Chapter 6 Lessons 1 and 2
Walter White's Math Lesson
Graphs of Normal Probability Distributions Lesson 1
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
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.