Download In Class Packet Work Chp 1-6

AP STATISTICS
Chp 1-2 Packet
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Page 2
Warm Ups
Page 6
Chp 1- 2 Chapter Outline
Page 8
M&M Data Collection
Page 9
Chp 2 Class Notes
Page 11 Chp 2 Group Quiz
Page 12 Chp 3 Chapter Outline
Page 14 Chp 3 Class Notes
Page 20 Chp 3 Classwork Smoking and Education
Page 21 Chp 3 Group Quiz
Page 22 Chp 3 Investigative Task
Page 25 Chp 4 Outline
Page 27 Chp 4 Class Notes
Page 31 Chp 4 Investigative Task
Page 34 Chp 4 Group Quiz
Page 35 Chp 5 Chapter Outline
Page 37 Chp 5 Class Notes
Page 39 Chp 5 Mooseburgers and McTofu
Page 40 Chp 5 Investigative Task Auto Safety
Page 43 Chp 5 Group Quiz
Page 45 Chp 6 Outline
Page 48 Chp 6 Notes
Page 52 Chp 6 Investigative Task
Page 55 Chp 6 Group Quiz
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Warm Ups:
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Warm Ups: (cont)
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Chapter Outline
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Warm Ups: (cont)
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Warm Ups: (cont)
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Warm Ups: (cont)
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Chapter 1: Stats Starts Here
Chapter 2: Data
1. Name three things you learned about Statistics in Chapter 1.
•
•
•
2. The authors claim that this book is very different from a typical mathematics textbook.
Would you agree or disagree, based on what you read in Chapter 1? Explain.
3. According to the authors, what are the “three simple steps to doing Statistics right?”
4. What do the authors refer to as the “W’s of data?”
5. Why must data be in context (the W’s)?
6. Explain the difference between a categorical variable and a quantitative variable. Give an
example of each.
Key Vocabulary:
Statistics
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ƒ data, datum
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ƒ variation
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ƒ individual
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ƒ respondent
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ƒ subject
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ƒ participant
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ƒ experimental unit
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ƒ observation
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ƒ variable
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ƒ categorical
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quantitative
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Calculator Skills:
enter data in a list
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change a datum
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e a datum
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name a new list
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clear a list
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delete a list
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recreate a list
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copy a list
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Class notes
Data
Chapter 2:
What are data?
In order to determine the context of data, consider the “W’s”

Who –

What (and in what units) –

When –

Where –

Why –

How –
There are two major ways to treat data:

A _______________ _______________ is used to answer questions about how cases fall into
categories. A categorical variable may be comprised of word labels, or it may use numbers as
labels.
Examples:

A _______________ _______________ is used to answer questions about the quantity of what is
being measured. A quantitative variable is comprised of numeric values.
Examples:
10
What is a statistic?
Are the numbers 17, 21, 44, 76 data?
Data must have ______ to be meaningful. The numbers listed above could be test scores, ages of a group
of golfers, or the uniform numbers of the starting backfield on the football team. Without ______ data
cannot be interpreted.
Suppose a Consumer Reports article (published in June 2005) on energy bars gave the brand name, flavor,
price, number of calories, and grams of protein and fat. Identify the following:

Who:

What:

When:

Where:

How:

Why:

Categorical variables:

Quantitative variables (with units):
A report on the Boston Marathon listed each runner’s gender, county, age, and time. Identify the
following:

Who:

What:

When:

Where:

How:

Why:

Categorical variables:

Quantitative variables (with units):
11
Chp 1-2 Quiz
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Chapter Outline
Chapter 3: Displaying and Describing
Categorical Data
1. According to the authors, what are the three rules of data analysis?
2. Explain the difference between a frequency table and a relative frequency table.
3. When is it appropriate to use a bar chart?
4. When is it appropriate to use a pie chart?
5. When is it appropriate to use a contingency table?
6. What does a marginal distribution show?
7. When is it appropriate to look at a conditional distribution?
8. What does it mean for two variables to be independent?
9. How does a segmented bar chart compare to a pie chart?
10. Explain what is meant by Simpson’s Paradox.
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Key Vocabulary:
ƒ frequency table
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ƒ relative frequency table
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ƒ distribution
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ƒ bar chart
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ƒ pie chart
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ƒ contingency table
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ƒ marginal distribution
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ƒ conditional distribution
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ƒ independent
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ƒ segmented bar chart
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Simpson’s Paradox
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Stats: Modeling the World – Chapter 5
Chapter 3 – Displaying and Describing Categorical Data
_______________ _______________ are often used to organize categorical data. Frequency tables
display the category names and the _______________ of the number of data values in each category.
_
_______________________ also display the category names, but they give the
_______________ rather than the counts for each category.
Color
Freq.
Blue
13
Red
7
Orange
11
Green
9
Yellow
8
Brown
7
TOTAL
55
Rel. Freq.
Percent
1.000
100%
A _______________ is often used to display categorical data. The height of each bar represents the
_______________ for each category. Bars are displayed next to each other for easy comparison. When
constructing a bar chart, note that the bars do not _______________ one another. Categorical variables
usually cannot be ordered in a meaningful way; therefore the order in which the bars are displayed is
often meaningless.
A _________ bar chart displays the proportion
of counts for each category.
M&M Color Distribution
14
13
11
Frequency
12
9
10
7
8
8
7
6
4
2
0
Blue
Red
Orange
Green
Yellow
Brown
Stats: Modeling the World – Chapter 5
The sum of the relative frequencies is _____.
M&M Color Distribution
30%
24%
Frequency
25%
20%
20%
16%
14%
13%
Yellow
Brown
13%
15%
10%
5%
0%
Blue
Red
Orange
Green
A _______________ _______________ is another type of display used to show categorical data. Pie
charts show parts of a whole. Pie charts are often difficult to construct by hand.
A _______________ _______________ shows two categorical variables together. The margins give the
frequency distributions for each of the variables, also called the ________
___ .
Examine the class data about gender and political view – liberal, moderate, conservative.
Liberal
Moderate
Conservative
TOTAL
Male
Female
TOTAL

What percent of the class are girls with liberal political views?

What percent of the liberals are girls?

What percent of the girls are liberals?

What is the marginal distribution of gender?
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Stats: Modeling the World – Chapter 5

What is the marginal distribution of political views?
A conditional distribution shows the distribution of one variable for only the individuals who satisfy
some condition on another variable.
The conditional distribution of political preference, conditional on being male:
Liberal
Moderate
Conservative
TOTAL
Male
The conditional distribution of political preference, conditional on being female:
Liberal
Moderate
Conservative
TOTAL
Female

What is the conditional relative frequency distribution of gender among conservatives?
If the conditional distributions are the same, we can conclude that the variables are not associated.
Therefore, they are _______________ of one another.
If the conditional distributions differ, we can conclude that the variables are somehow associated.
Therefore, they are _______________ of one another.

Are gender and political view independent?
A segmented bar chart displays the same information as a pie chart, but in the form of bars instead of
circles. Comparing segmented bar charts is a good way to tell if two variables are independent of one
another or not.
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Stats: Modeling the World – Chapter 5
Gender vs. Political Preference
1
0.9
0.8
Percent
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Male
Female

Explain how the graph on the left violates the “area principle.”

Explain what is wrong with the graph below.
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Stats: Modeling the World – Chapter 5
Averaging one variable across different levels of a second variable can lead to
______________________________. Consider the following example:
It’s the last inning of an important game. Your team is a run down with the bases loaded and two outs.
The pitcher is due up, so you’ll be sending in a pinch-hitter. There are 2 batters available on the bench.
Whom should you send in to bat?

Player
Overall
A
33 for 103
B
45 for 151
Compare A’s batting average to B’s batting average. Which player appears to be the better
choice?
Does it matter whether the pitcher throws right- or left-handed?

Player
Overall
vs LHP
vs RHP
A
33 for 103
28 for 81
5 for 22
B
45 for 151
12 for 32
33 for 119
Compare A’s batting average vs. a left-handed pitcher to B’s. Compare A’s batting average
against a right-handed pitcher. Which player appears to be the better choice?
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Stats: Modeling the World – Chapter 5
Pooling the data together loses important information and sometimes leads to the wrong conclusion.
We always should take into account any factor that might matter.
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Stats: Modeling the World – Chapter 5
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Stats: Modeling the World – Chapter 5
Group Quiz Chp 3
Chp 3 Investigative Task
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Stats: Modeling the World – Chapter 5
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Stats: Modeling the World – Chapter 5
Investigative Task Answer:
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Investigative Task Rubric
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Stats: Modeling the World – Chapter 5
Chp 4 Outline: Displaying Quantitative Data
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Stats: Modeling the World – Chapter 5
1. What is meant by a distribution?
2. Explain the difference between a histogram and a relative frequency histogram.
3. In what ways are histograms similar to stem-and-leaf displays?
4. Name some advantages and disadvantages of stem-and-leaf displays.
5. When is it more appropriate to use a histogram rather than a stem-and-leaf display?
6. Name some advantages and disadvantages of dotplots.
7. When describing a distribution, what three things should you always mention?
8. What should you look for when describing the shape of a distribution?
9. In general, what is meant by the center of a distribution?
10. In general, what is meant by the spread of a distribution?
11. When is it appropriate to use a time plot to display quantitative data?
12. What is meant by re-expressing or transforming data? What is the purpose of re-expressing
or transforming data?
Key Vocabulary:
Distribution
histogram
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Stats: Modeling the World – Chapter 5
relative frequency
histogram
stem-and-leaf display
dotplot
shape
center
spread
mode
unimodal
bimodal
multimodal
uniform
Symmetric
Tail
skewed
outliers
gaps
time plot
re-expressing data
Calculator Skills:
display a histogram
Sort
A(
ƒ
ƒ
ƒ
d
isplay a
histogram
ƒ
Chp
4 Notes: Displaying Quantitative Data
SortA (
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Stats: Modeling the World – Chapter 5
A _______________ or _______________ is often used to display categorical data. These types of
displays, however, are not appropriate for quantitative data. Quantitative data is often displayed using
either a _______________ _______________ or a _______________
In a histogram, the interval corresponding to the width of each bar is called a _______________ A
histogram displays the bin counts as the height of the bars (like a bar chart). Unlike a bar chart,
however, the bars in a histogram _______________ one another. An empty space between bars
represents a _______________ in data values. If a value falls on the border between two consecutive
bars, it is placed in the bin on the _______________.
# of Students
Shoe Sizes of AP Stat Students
6
6.5
7
7.5
8
8.5
9
9.5
10 10.5 11 11.5 12 12.5 13
Shoe Size
A _______________ _______________ histogram displays the proportion of cases in each bin instead of
the count.
Histograms are useful when _____________________________________________, and they can easily
be constructed using a graphing calculator. A disadvantage of histograms is that they _______________
______________________________.
Be sure to choose an appropriate bin width when constructing a histogram. As a general rule of thumb,
your histogram should contain about _______ bars.
A _______________ _______________ is similar to a histogram, but it shows_______________
_______________ rather than bars. It may be necessary to _______________ stems if the range of data
values is small.
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Stats: Modeling the World – Chapter 5
Number of Pairs of Shoes Owned
0
0
1
1
2
2
3
3
KEY:
A _______________ _______________ stem-and-leaf plot can be useful when _______________ two
distributions.
Number of Pairs of Shoes Owned
Male
Female
.
0
0
1
1
2
2
3
3
KEY:
The stems of the stem-and-leaf plot correspond to the _______________ of a histogram. You may only
use ______ digit for the leaves. Round or truncate your values if necessary.
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Stats: Modeling the World – Chapter 5
Stem-and-leaf plots are useful when working with sets of data that are __________________
__________________ in size, and when you want to display _______________ _______________.
How would you setup the following stem-and-leaf plots?
 quiz scores (out of 100)
 student GPA’s
 student weights
 SAT scores
 weights of cattle (1000-2000 pounds)
_____________ may also be used to display quantitative variables. Dot plots are useful when working
with ____________ sets of data.
Guess Your Teacher's Age
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Predicted Age
When describing a distribution, you should tell about three things: _______________ ,
_______________, and _______________. You should also mention any unusual features, like
_______________ or _______________.
Identify the shapes of the following distributions:
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Stats: Modeling the World – Chapter 5
When comparing two or more distributions, compare the _______________ , _______________, and
_______________, and compare any _______________ features. It is important, when comparing
distributions, that their graphs be constructed using the same _______________.
You can sometimes make a skewed distribution appear more symmetric by _______________ (or
transforming) your data.
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Stats: Modeling the World – Chapter 5
Chp 4 Investigative Task (Like #6 on AP test)
Investigative Task Answer:
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Stats: Modeling the World – Chapter 5
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Stats: Modeling the World – Chapter 5
Investigative Task Rubric:
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Stats: Modeling the World – Chapter 5
Chapter 4 Group Quiz
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Stats: Modeling the World – Chapter 5
Chapter Outline 5:
Describing Distributions Numerically
1. Explain the difference between range and interquartile range. Why is the
interquartile range often a better measure of the spread of a distribution?
2. What are some advantages of boxplots?
3. What are some disadvantages of boxplots?
4. When is it more appropriate to use the mean as a measure of center rather than the median?
Why?
5. When is it more appropriate to use the median as a measure of center rather than the mean?
Why?
6. When do the mean and median have the same value?
7. Describe the relationship between variance and standard deviation.
Key Vocabulary
Center
ƒ
spread
ƒ
midrange
ƒ
median
ƒ
range
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Stats: Modeling the World – Chapter 5
ƒ
quartile
ƒ
interquartile range
ƒ
percentile
ƒ
five-number summary
ƒ
boxplot
Calculator Skills:
Boxplot
Modified boxplot
1 Var Stats
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Stats: Modeling the World – Chapter 5
Chp 6 Notes: Describing Distributions Numerically
When describing distributions, we need to discuss _______________, _______________, and
_______________. How we measure the center and spread of a distribution depends on its
_______________. The center of a distribution is a “typical” value. If the shape is unimodal and
symmetric, a “typical” value is in the _______________. If the shape is skewed, however, a “typical”
value is not necessarily in the middle.
For _______________ distributions, use the _______________ to determine the _______________ of
the distribution and the _______________ to describe the _______________ of the distribution.
The median:

is the _______________ data value (when the data have been _______________) that divides
the histogram into two equal _______________

has the same _______________ as the data

is _______________ to outliers (extreme data values)
The range:

is the difference between the _______________ value and the _______________ value

is a _______________, NOT an _______________

is _
___to outliers
The interquartile range (IQR):

contains the _______________ of the data

is the difference between the _______________ and _______________ quartiles

is a _______________, NOT an _______________

is _______________ to outliers
The _______________ _______________ gives: _______________, _______________,
_______________, _______________, _______________,
A graphical display of the five-number summary is called a _______________.
How many hours, on average, do you spend watching TV per week? ______ Collect data from the
entire class and record the values in order from smallest to largest. Calculate the five-number summary:
Construct both a histogram and a boxplot (using the same scale). Compare the displays.
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Stats: Modeling the World – Chapter 5
Average Number of Hours per Week Spent Watching TV
For _______________ distributions, use the _________________ _to determine the _______________
of the distribution and the _______________ to describe the _______________ of the distribution.
The mean:

is the arithmetic _______________ of the data values

is the ____

has the same _______________ as the data

is _______________ to outliers

is given by the formula
_ of a histogram
The standard deviation:

measures the “typical” distance each data value is from the _______________

Because some values are above the mean and some are below the mean, finding the sum is not
useful (positives cancel out negatives); therefore we first _______________ the deviations, then
calculate an _______________ _______________ . This is called the _______________. This
statistics does not have the same units as the data, since we squared the deviations. Therefore,
the final step is to take the _______________ of the variance, which gives us the
_______________
.

is given by the formula

is _______________
_to outliers, since its calculation involves the _______________
Find the mean and standard deviation of the average number of hours spent watching TV per week for
this class.
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Stats: Modeling the World – Chapter 5
Classwork Chp 5
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Stats: Modeling the World – Chapter 5
Investigative Task Auto Safety
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Stats: Modeling the World – Chapter 5
Investigative Task Answer:
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Stats: Modeling the World – Chapter 5
Investigative Task Rubric:
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Chp 5 Group Quiz
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Stats: Modeling the World – Chapter 5
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Stats: Modeling the World – Chapter 5
Chapter Outline 6: The Standard Deviation
as a Ruler and the Normal Model
1. What unit of measurement is used to describe how far a set of values are from the mean?
2. Explain how to standardize a value.
3. Briefly describe why standardized units are used to compare values that are measured using
different scales, different units, or different populations.
4. How does adding or subtracting a constant amount to each value in a set of data affect the
mean? Why does this happen?
5. How does multiplying or dividing a constant amount by each value in a set of data (also
called rescaling) affect the mean? Why does this happen?
6. How does adding or subtracting a constant amount to each value in a set of data affect the
standard deviation? Why does this happen?
7. How does multiplying or dividing a constant amount by each value in a set of data (also
called rescaling) affect the standard deviation? Why does this happen?
8. How does standardizing a variable affect the shape, center, and spread of its distribution?
9. In what way does a z-score give an indication of how unusual a value is?
10. How would you describe the shape of a normal curve? Draw several examples.
11. Where on the normal curve are inflection points located?
12. When is it appropriate to use a normal model to model a set of data?
13. Explain the difference between y and μ .
14. Explain the difference between s and σ .
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Stats: Modeling the World – Chapter 5
15. Briefly explain the 68-95-99.7 Rule.
16. What is a percentile?
17. Is there a difference between the 80th percentile and the top 80%? Explain.
18. Describe two methods for assessing whether or not a distribution is approximately normal.
Key Vocabulary
standard deviation
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standardized value
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rescaling
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z-score
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normal model
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parameter
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statistic
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standard Normal model
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68-95-99.7 Rule
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normal probability plot
Calculator Skills:
normalpdf(
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normalcdf(
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invNorm(
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normal probability plot
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-1E99 and 1E99
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N( μ
,σ )
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Chapter 6: Normal Percentiles
1. Suppose the class took a 40-point quiz. Results show that a mean score of 30, median 32, IQR 8,
standard deviation 6, min 12 and lower quartile 27. You got a 35. What happens to each of the
statistics if…
a. I decide to weight the quiz as 50 points by adding 10 points to each score. Your score is
now 45.
x=
M=
IQR =
s=
min =
Q1=
b. I decide to weight the quiz as 80 points by doubling each score. Your score is now 70.
x=
M=
IQR =
s=
min =
Q1=
c. I decide to count the quiz as 100 points by doubling each score, then adding 20 points.
Your score is now 90.
x=
M=
IQR =
s=
min =
Q1=
2. Consider the three athletes’ performances shown below in a 3-event competition. Note that each
person finishes first, second, and third one time. Who deserves the gold medal? And who gave the
most remarkable performance of the competition?
Competitor
A
B
C
Mean
St Dev
100 m Dash
10.1 sec
9.9 sec
10.3 sec
10 sec
0.2 sec
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Event
Shot Put
66’
60’
63’
60’
3’
Long Jump
26’
27’
27’ 3”
26’
6”
3. Sketch a Normal model for each of the following:
a. Birthweights of babies, N(7.6 lb, 1.3 lb)
b. ACT scores at a certain college N(21.2, 4.4)
4. Use your knowledge of Normal models to guess plausible standard deviations for each of the
following variables.
a. Height of 16-yr old girls
b. Weight of high school boys
c. Current price of gasoline
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5. Suppose a Normal model describes the fuel efficiency of cars currently registered in Maryland. The
mean is 24 mpg, with a standard deviation of 6 mpg.
a. Sketch the Normal model.
b. What percent of all cars get less than 15 mpg?
c. What percent of all cars get between 20 and 30 mpg?
d. What percent of cars get more than 40 mpg?
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e. Describe the fuel efficiency of the worst 20% of all cars.
f.
What gas mileage represents the third quartile?
g. Describe the gas mileage of the most efficient 5% of all cars.
h. An ecology group is lobbying for a national goal calling for no more than 10% of all cars
to be less than 20 mpg. If the standard deviation does not change what average fuel
efficiency must be attained?
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Investigative Task Answer:
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Group Quiz Chp 6
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