Get out your Standard Normal WS!
Today’s Objectives:
You will be able to use a four-step method to
solve Normal distribution problems.
Warm Up
Use Table A to answer the following questions.
1. 𝑧 is between -1.24 and -0.32
Use Table A to answer the following questions. In
each case sketch a standard Normal curve with your
value of 𝒛 marked on the axis.
2. The 63rd percentile of the standard Normal
distribution.
3. 75% of all observations are greater than 𝑧.
Homework Check
Homework Check
Normal Distribution Calculations
Steps to find a percentile in problems involving
Normal distributions.
Step 1: State the problem in terms of the observed
variable 𝑥.
Step 2: Standardize and draw a picture.
Step 3: Use the table.
Step 4: Write your conclusion in the context of the
problem.
Normal Method Example
When Tiger Woods 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?
Step 1: State the problem
Let 𝑥 =
𝜇 =
𝜎 =
We want the proportion of drives
with 𝑥 ≥ ____________.
Step 2: Standardize
What is the 𝑧-score of 290?
Step 3: Use Table A
Find the proportion of observations less
than (to the left of) -1.75 and then find the
area to the right to answer the question.
Convert this decimal to a percent.
Step 4: Conclusion
About _______% of Tiger Woods’
drives on the range travel at least
290 yards.
Tiger Example Part 2
What percent of Tiger’s drive travel
between 305 and 325 yards?
Follow the four-step method.
Table A—In Reverse
Steps to find a variable (x) in problems
involving Normal distributions where the
percentile is given.
Step 1: State the problem and draw a picture
Step 2: Use Table A
Step 3: “Un-standardize”
Step 4: Conclusion
Reverse Example
When Tiger hits his driver, the distance the ball
travels follows a Normal distribution with mean
304 yards and standard deviation 8 yards.
What distance would a ball have to travel to be
at the 80th percentile of Tiger’s drive lengths?
Step 1: State and Draw
Let 𝜇 =
𝜎 =
We want to find the drive distance 𝑥.
Step 2: Table A
Look in Table A for the entry closest to 0.80.
Step 3: “Un-Standardize”
𝑥−𝜇
𝑧=
𝜎
Step 4: Conclusion
A golf ball would have to travel
____________ yards to be at the 80th
percentile of Tiger’s drive length
distribution.
Running a Mile—Try One!
During World War II, physical training was
required for male students in many colleges, as
preparation for military service. A study of
12,000 able-bodied male students at the
University of Illinois found that their times for
the mile run had mean 7.11 minutes and
standard deviation 0.739 minutes. The
distribution of times was roughly Normal.
Try One!
Here are some sample questions one might ask
about this distribution of times. Follow the
four-step method to answer these questions.
a) About how many of the 12,000 male
students ran a mile in less than 5 minutes?
b) What is the 93rd percentile in the mile run
time distribution?
c) Do you think students today could match
this performance? Justify your answer.
Ticket Out The Door
Write down the four-step method using
Table A when finding a percentile.
Then,
Write down the four-step method using
Table A in reverse when finding an
unknown variable.
Homework
Four-Step Method Worksheet
Due Friday