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AP Stats
Review
Mrs. Daniel
Alonzo & Tracy Mourning Sr. High
[email protected]
Agenda
1.
2.
3.
4.
5.
6.
AP Stats Exam Overview
AP FRQ Scoring & FRQ: 2016 #1
Distributions Review
FRQ: 2015 #6
Distribution Mash-Up
FRQ:
AP Stats
Exam
Exam Format
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Two 90 minute sections
Reference Sheet and Calculator!
First section: 40 multiple choice questions
Second section: 6 free response questions
(FRQs)
– First 5 FRQs = 12 minutes each
– FRQ # 6 : Investigative task for 30 minutes
Scoring
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Exam is scored out of 100 points.
Each MC is worth 1.25 points
Each FRQ (#1-5) is worth 7.5 points
FRQ #6 is worth 15 points
What’s on the Exam?
Exploring Data (20-30%): Describing patterns and
departures from patterns (CH. 1-3)
Sampling and Experimentation (10-15%): Planning and
conducting a study (CH. 4)
Anticipating Patterns (20-30%): Exploring random
phenomena using probability and simulation (CH. 5-7)
Statistical Inference (30-40%): Estimating population
parameters and testing hypotheses (CH 8-12)
FRQ Scoring
• Each question is scored from 1 to 4.
• The raw score is then multiplied by 1.875 to
determined the scaled score.
• The numerical score is derived from a series
of:
– Essentially Correct
– Partially Correct
– Incorrect
FRQ Scoring
Sample Scale for a 4 part question.
FRQ Scoring
AP Stats 2016 Scores
Thursday,
May 11, 2017
NOON
FRQ: 2016 #1
You have 12 minutes. Go!!!
Solution
Part a:
The distribution of Robin’s tip amounts is skewed to
the right. There is a gap between the largest tip
amount (between $20 to 22.50) and the second
largest tip amount (between $12.50 and $15
interval). The largest tip amount appears to be an
outlier. The median tip amount is between $2.50
and $5. Robin’s tip amounts vary from a minimum
of $0 to $2.50 to a maximum of between $20 and
$22.50. About 78% of tip amounts are between $0
and $5.
Scoring
Solution
Part b:
If the $8 tip had really been $18, the total would
increase by $10. Then, we would divide by 60,
so the increase to the mean would be about 17
cents.
The median would not change, since both $8
and $18 are greater than the current median.
Scoring
Scoring Guidelines
Distributions
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Normal
Binomial
Geometric
Sampling
Normal Distributions
• All Normal curves are symmetric, single-peaked, and bellshaped
• A Specific Normal curve is described by giving its mean µ
and standard deviation σ.
Two Normal curves, showing the mean µ and
standard deviation σ.
Normal Distributions
• We abbreviate the Normal distribution with mean µ and
standard deviation σ as N(µ,σ).
• Any particular Normal distribution is completely specified by
two numbers: its mean µ and standard deviation σ.
• The mean of a Normal distribution is the center of the
symmetric Normal curve.
• The standard deviation is the distance from the center to the
change-of-curvature points on either side.
The 68-95-99.7 Rule
Although there are many different sizes and shapes of Normal
curves, they all have properties in common.
The 68-95-99.7 Rule (“The Empirical Rule”)
In the Normal distribution with mean µ and standard
deviation σ:
•Approximately 68% of the observations fall
within σ of µ.
•Approximately 95% of the observations fall
within 2σ of µ.
•Approximately 99.7% of the observations fall
within 3σ of µ.
Binomial v. Geometric
• The primary difference between a binomial
random variable and a geometric random
variable is what you are counting.
• A binomial random variable counts the
number of "successes" in n trials.
• A geometric random variable counts the
number of trials up to and including the first
"success."
Binomial vs. Geometric
The Binomial Setting The Geometric Setting
1. Each observation falls into 1. Each observation falls into
one of two categories.
one of two categories.
2. The probability of success 2. The probability of success
is the same for each
is the same for each
observation.
observation.
3. The observations are all
3. The observations are all
independent.
independent.
4. There is a fixed number n
of observations.
4. The variable of interest is
the number of trials
required to obtain the 1st
success.
FRQ Answers Must Include:
1. Name of distribution
Geometric, Binomial
2. Parameters
Binomial: X (define variable), n & p
Geometric: X (define variable), p
3. Probability Statement
Ex: P (X = 7) or P (X ≥ 3)
4. Calculation and p-value
Calculator notation is okay, but needs to be
labeled.
5. Solution interpreted in context.
Let’s Practice…
Twenty-five percent of the customers entering a grocery store
between 5 p.m. and 7 p.m. use an express checkout. Consider
five randomly selected customers, and let X denote the
number among the five who use the express checkout. What is
the probability that two customers used the express check
out?
Twenty-five percent of the customers entering a grocery store
between 5 p.m. and 7 p.m. use an express checkout. Consider
five randomly selected customers, and let X denote the
number among the five who use the express checkout. hat is
the probability that two customers used the express check
out?
Binomial Distribution
N= 5
P = 0.25
X = # of people use express
P (X =2)
Twenty-five percent of the customers entering a grocery
store between 5 p.m. and 7 p.m. use an express checkout.
Consider five randomly selected customers, and let X denote
the number among the five who use the express checkout.
What is the probability that two customers used the express
check out?
binompdf(5, 0.25, 2) = .2637
5= number of customers
0.25= probability of success
2= number of successes desired
There is a 26.37% chance that exactly 2 customers
will use the express checkout lane between 5pm and
7pm.
Sampling Distribution
Population Distributions vs. Sampling
Distributions
There are actually three distinct distributions involved when we
sample repeatedly and measure a variable of interest.
1) The population distribution gives the values of the variable for
all the individuals in the population.
2) The distribution of sample data shows the values of the variable
for all the individuals in the sample.
3) The sampling distribution shows the statistic values from all the
possible samples of the same size from the population.
Sample Proportion Formulas
 pˆ 
p(1  p)
n
The sample size MUST be less than 10% of the total
population.
Sample Means Formulas
x  
Notes: The sample size must be less than 10% of the
population to satisfy the independence condition. The
mean and standard deviation of the sample mean are true
no matter the same of the population distribution.
Sample Distributions & Normality:
Sample Distributions & Normality:
Sample Distributions & Normality:
HOW LARGE IS LARGE ENOUGH?
If the Population shape
is….
Normal
Slightly Skewed
Heavily Skewed
Unknown
Minimum Sample Size to
assume Normal
0
15
30
30
FRQ: 2015 #6
You have 22 minutes. Go!!!
Scoring Rubric
Scoring Rubric
Scoring Rubric
Scoring Rubric
Distributions
Mash Up
SKIP: Distributions Mash Up
2B.
3B (bonus!!)
6A
Distributions Mash Up
1. a. 0.019
2. a. normalcdf ( 140, inf, 120, 10.5) = 0.0287
c. binompdf (3, .5, 0) = 0.064
3. a. normpdf (850, inf, 840, 7.9) = 0.064
4. a. $0.70
b. 715 plays
c. Normcdf ( 500, inf, 700, 92.79) = 0.9844
Distributions Mash Up
5. a. geometcdf (.1, 4, 100) = 0.729
b. binompdf (20, .1, 2) = 0.285
c. binomcdf (104, .1, 21) = 0.001368
6. b. normcdf (4, inf, 3.9,
1.1
)
40
= 0.282659
OR normcdf (160, inf, 156, 6.987)
7. a. 5 questions
b. 18 + .2(7) - .8(7)(.25)
c. binomcdf (7, 0.2, 3, 7) = 0.148
FRQ: 2011 #6
You have 25 minutes. Go!!!