Download Density and normal curves

Density Curves
A density curve
- is always on or above the horizontal axis
- has an area of exactly one
We use different symbols for the mean and standard deviation of a density curve.
mean - 
Examples of density curves
standard deviation - 
Density Curves
Example 1:
The time that a person waits for the elevator by the bookroom is uniformly
distributed with a mean of 1.5 minutes and a range of 1 minute.
a. Construct a distribution for the above information.
b. What percent of the observations would involve a wait time of less than 1.25 minutes?
c. What percent of the observations would involve a wait time of between 1.2 and 2 minutes?
Density Curves
Example 2:
Consider the population that consists of all soft contact lenses made by a particular
manufacturer and define the variable x = thickness (in mm). Suppose that a reasonable
model for the population distribution is the one shown below:
a. Verify that the total area under the density
curve is equal to 1.
b. What percent of the contact
lenses have thickness less than
.20mm? Less than .10mm?
c. What percent of the contact lenses
are within .05 mm of the mean of
thickness?
The Normal Curve
Symmetrical, single peaked, bell-shaped density curve
Used for : SAT scores, heights, intelligence, etc.
The Normal Curve
Empirical Rule (or 68-95-99.7 rule)
• Approximately 68% of the observations are
Can ONLY be used
within 1 of 
with
normal
curves!
• Approximately 95% of the observations are
within 2 of 
• Approximately 99.7% of the observations
are within 3 of 
The Normal Curve
Empirical Rule (or 68-95-99.7 rule)
68%
2.35%
2.35%
13.5%
34%
34%
0.15%
13.5%
0.15%
95%
99.7%
The Normal Curve
Example: page 133: #26