Using the Empirical Rule

1
Using the Empirical Rule
2
(No Transcript)
3
Remember Normal Distributions

• These are special density curves.
• They have the same overall shape
• Symmetric
• Single-Peaked
• Bell-Shaped
• They are completely described by giving its mean
  (?) and its standard deviation (?).
• We abbreviate it N(?,?)

4
Normal Curves.

• Changing the mean without changing the standard
  deviation simply moves the curve horizontally.
• The Standard deviation controls the spread of a
  Normal Curve.

5
Standard Deviation

• Its the natural measure of spread for Normal
  distributions.
• It can be located by eye on a Normal curve.
• Its the point at which the curve changes from
  concave down to concave up.

6
Empirical Rule (68-95-99.7 Rule)

• In the Normal distribution with mean (?) and
  standard deviation (?)
• Within 1? of ? 68 of the observations
• Within 2? of ? 95 of the observations
• Within 3? of ? 99.7 of the observations

7
Scores on the Wechsler adult Intelligence Scale
(a standard IQ test) for the 20 to 34 age group
are approximately Normally distributed. N(110,
25).

• What percent are between 85 and 135?
• What percent are below 185?
• What percent are below 100?

8
Standard Normal Distribution

• It is the Normal distribution with mean 0 and
  standard deviation 1.
• If a variable x has any Normal distribution N(?,
  ?), then the standardized variable
• has the standard Normal distribution.

9
A standard Normal table give the area under the
curve to the left of z. Find the area to the
left of z 0.21
10
Using the chart

• Find P(zlt1.23)
• Find P(z gt 2.01)

11
More examples

• Find P(zlt -0.13)
• Find P(z gt -1.72)

12
More examples

• Find P(-1.56 lt z lt 1.01)
• Find P(-2.23 lt z lt -0.27)

13
Try the following

• P(z lt 1.39)
• P(z gt -2.15)
• P(-0.56 lt z lt 1.81)

14
Find the z-score that correlates with the 20th
percentile.
15
For what z-score are 45 of all observations
greater than z?
16
Homework

• Correction to Assignment Sheet
• Page 131 (43-52)