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Unit 6
Section 6-4 – Day 1
Section 6-4
6-4: Applications of the Normal
Distribution

A standard normal distribution can often be
used to solve practical application problems.

In order to use the normal distribution, the
variables must be normally (or approximately
normally) distributed.

In order to solve these problems, first translate
the values of the variable into z values, then
find the areas under the standard normal
distribution. Hint: Drawing a picture will help!
Section 6-4
Formula for a z-score
Z =
value – mean
standard deviation
Section 6-4

Example 1:
The mean number of hours an American worker
spends on the computer is 3.1 hours per
workday. Assume the standard deviation is 0.5
hours. Find the percentage of workers who
spend less than 3.5 hours on the computer.
Assume the variable is normally distributed.
Step 1: Draw a figure to represent the situation
Step 2: Find the z value corresponding to 3.5
Step 3: Find the area
Section 6-4

Example 2:
Each month, an American household generates an
average of 28 pounds of newspapers for garbage or
recycling. Assume the standard deviation is 2
pounds. If a household is selected at random, find
the probability of its generating…
a)
Between 27 and 31 pounds per month
b)
More than 30.2 pounds per month.
Assume the variable is approximately normally
distributed.
Section 6-4
 Example
3:
The American Automobile Association
reports that the average time it takes to
respond to an emergency call is 25 minutes.
Assume the variable is approximately
normally distributed and the standard
deviation is 4.5 minutes. If 80 calls are
selected at random, how many will be
responded to in less than 15 minutes?
Section 6-4
Homework:
 Pg
316
 Applying
the Concepts (1 – 4)
 Exercises (1 – 4)