Session Packet #3
Supplemental Instruction
Iowa State University
Leader: Carly
Course: Stat 226
Instructor:
Date: 2/4/13
Opening Activity: True/False Quiz
For questions 1-15, answer true or false. If the statement is false, change it in a way that makes
it true. Try to complete this quiz on your own without using your notes.
____ 1.) A statistical model is a breakdown of variation into a predictable pattern and the
remaining variation. True
____ 2.) Adding the probabilities associated with all outcomes of a random event yields 1. True
____ 3.) Statistical models are only adequate if they predict reality exactly. False; approximately
____ 4.) A random variable describes the probabilities for an uncertain, past numerical outcome
of a random process. False; future
____ 5.) A random variable that takes on any value in an interval is called a discrete random
variable. False; continuous
____ 6.) The Probability Distribution of a Random Variable is a function that assigns
probabilities to each possible outcome of the random variable. True
____ 7.) The area under any density curve is always equal to 1. True
____ 8.) Every normally distributed random variable follows a probability distribution that is
characterized by the mean µ and the variance σ2. True
____ 9.) The larger the σ2, the less variability in our data. False; more
____ 10.) To denote that a variable follows a normal distribution, we use X~N(µ,σ2). True
____ 11.) The normal distribution is symmetric about its variance σ2. False; mean µ
____ 12.) The 68-95-99.7 Rule, also known as the Empirical Rule, says that approximately 68%
of the data in a normal distribution fall within a range of (µ-2σ, µ+2σ). False; 95%
____ 13.) 13.5% of the data in a normal distribution will be between µ+σ and µ+2σ, according to
the Empirical Rule. True
____ 14.) The standard normal distribution has a mean of 0 and a variance equal to 1. True
____ 15.) The lifespan of U.S. citizens follows a normal distribution with µ = 75 and a standard
deviation of 2 years. The middle 95% of all U.S. citizens live between (75 - 2*(2)2) and
(75+2*(2)2). False; (75 – 2*(2)) and (75 + 2*(2))
1060 Hixson-Lied Student Success Center  515-294-6624  sistaff@iastate.edu  http://www.si.iastate.edu
Labeling Activity: The Normal Distribution Model
On the figure of the normal distribution model below, label each tick mark on the
x-axis, the percentages associated with the Empirical Rule, and the percentages
that represent the areas underneath the curve.
Probability Activity: The Normal Distribution
After finishing school, you decide to open a sunglass-selling stand. Your stand is only open
during the summer. You know that based on other sunglass selling stands in the area, that the
overall summer sales of sunglasses for this area is approximately normally distributed with a
mean of 500 sunglasses and a standard deviation of 65 sunglasses. Assuming your stands’ sales
will follow the same distribution, use the 68-95-99.7 Approximation Rule to find the answers to
the following:

What is the proper notation for this distribution?
X corresponds to the random variable for number of sunglasses sold
X~N(500,652)

What is the probability that you sell more than 695 sunglasses?
1.) Determine how spread apart the number 695 is from the mean, 500.
695 – 500 = 195 sunglasses sold
2.) Determine the number of standard deviations between 695 and 500.
195 / 65 = 3 standard deviations
3.) Sketch the distribution and shade the area under the curve in which we are interested.
4.) Use the 68-95-99.7 Approximation Rule to determine the area shaded under the
curve.
1 − 0.997
𝑃=
= 0.0015 = 0.15%
2

Your goal for the first summer is to sell as many sunglasses as the middle 95% of all such
stands. Specify the range in which the number of glasses that you sell over the summer
has to fall inside.
1.) Sketch the distribution and shade the area for which the middle 95% of data should
be.
2.) Determine the number of standard deviations above the mean and the number of
standard deviations below the mean using the Approximate Rule.
(µ-2σ, µ+2σ)
3.) Calculate the range.
500 – 2(65) = 370
500 + 2(65) = 630
370 to 630 sunglasses

What price must you charge to sell enough sunglasses to fall at the 2.5th percentile but
still make at least $9,250?
1.) Determine how far away the 2.5th percentile is from the mean.
2.5th percentile corresponds to 2.5%
100% - 2(2.5%) = 95%
95% corresponds to 2 standard deviations below and above the mean. Therefore, the
2.5th percentile (since it is on the left side of the mean) corresponds to 2 standard
deviations below the mean.
2.) Determine the number of sunglasses that are 2 standard deviations less than the mean.
500 – 2(65) = 370 pairs of sunglasses
3.) Determine the price per pair of sunglasses if we are to fall at the 2.5th percentile but
still make at least $9250.
$9250 / 370 pairs = $25 per pair
Closing Topic: Study Strategy
Your first Statistics 226 exam is in two and a half weeks. It is time to start thinking about what
study strategies work best for you. One option is to create checklists. List reading assignments,
major ideas, definitions, and formulas.
Here is an example of what you have learned thus far in Chapter 12:
 Definition of Statistical Model
 Definition of Random Variable
 Continuous Random Variable vs. Discrete Random Variable (plus examples)
 Fundamental Properties for Probability (2 of them)
 Probability Notation
 Definition of Probability Distribution of a Random Variable
 Properties of a Normal Distribution of a Random Variable (mean, variance, shape, area)
 Definitions of Mean and Variance
 Notation of a Normal Distribution
 68-95-99.7 Rule (Empirical Rule/ Approximation Rule)
 The Normal Distribution Model (slide 16)
Remember, this checklist is not an all-inclusive review sheet. It is merely a to-do list. Try going
back in your notes to make a check-list for Chapters 1-4. Once you’ve created your check list, go
through each item in depth in preparation for your exam.