Download Notes: Applications of 3.2 Normal Distributions

Chapter 3
Modeling Distributions of Data
3.2 Normal Distributions Applications of Normal Distributions
On the driving range, Tiger Woods practices his swing with a
particular club by hitting multiple golf balls. When Tiger hits his
driver, the distance the ball travels follows a Normal distribution
with mean 304 yards and standard deviation 8 yards. What
percent of Tiger’s drives travel at least 290 yards? What percent
of Tiger’s drives travel between 305 and 325 yards?
Solving Problems Involving Normal Distributions
Step 1: State the problem in terms of the observed variable x.
Step 2: Standardize and draw a picture. Standardize x to restate
the problem in terms of a standard Normal variable z. Draw a
picture to show the area of interest under the standard Normal
curve.
Step 3: Use the table. Find the required area under the standard
Normal curve using Table A and the fact that the total area
under the curve is 1.
Step 4: Conclusion. Write your conclusion in the context of the
problem.
Example #1a – For us 
On the driving range, Tiger Woods practices his swing with a
particular club by hitting multiple golf balls. When Tiger hits his
driver, the distance the ball travels follows a Normal distribution
with mean 304 yards and standard deviation 8 yards.
What percent of Tiger’s drives travel at least 290 yards?
Example #1b – For you 
On the driving range, Tiger Woods practices his swing with a
particular club by hitting multiple golf balls. When Tiger hits his
driver, the distance the ball travels follows a Normal distribution
with mean 304 yards and standard deviation 8 yards.
What percent of Tiger’s drives travel between 305 and 325
yards?
Guided Practice: Examples #2a - #3c
Finding a Value, Given a Proportion
•Sometimes we may want to find the observed value that
corresponds to a given percentile. To do this, use Table A
backwards.
•Find the given proportion in the body of the table, read the
corresponding z from the left column and top row, then
“unstandardize” to get the observed value.
•Huh? Let’s look at an example.
Example #1c
What distance would a ball have to travel to be at the 80th
percentile of Tiger’s drive lengths?
Guided Practice: Examples #2def, #3def