Download standard deviation of 100

Stats Day 15
The Normal Model
DO NOW
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ACT #30, 31
Quick Z-Score
Review
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A school is judging its soccer student
scholarships based on number of goals scored
in the season to incentivize the high scoring
forwards to attend the school.
It says that they will give a scholarship to
students who score more than 2 standard
deviations above the mean of 21.4 goals with
a standard deviation of 3.7. What does David
need to score in the season to get the
scholarship?
The Normal Model
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Being able to represent the z-scores
as a distribution
• (concept)
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Using z-scores to understand
probability (percentiles)
• (application)
Z-score as a shift and
rescale of distribution
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When we make a z score, we take each data
point and subtract a number (the mean)
What would happen to the graph y=x if we subtracted 1 from each x
value y=(x-1)?
What changes?? We shift everything over (mean becomes 0)
We subtract EVERY VALUE by that number
What does not change??
SPREAD: Standard Deviation, Range, IQR
Shift and Rescale
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When we make a z score, we also take
each data point and divide by a number
(the standard deviation)
CHANGING OUR SCALE TO
STANDARD DEVIATION
The Normal
Distribution
Standard Deviation
MEAN
Drawing Normal
Models
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Notation: N ( mean, standard dev )
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Example: N(18,3)
Sketch the Normal
Distribution
1) N(500, 100)
• 2) N(100, 16)
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Knowing Extremes
Normal models show us how extreme a
value is by showing how LIKELY it is to
find a value that far from the mean
Sketch and Describe
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Sketch the distribution of the
birthweights of babies: N(7.6lb, 1.3lb)
We are 68% sure that the baby will be born between
______lb and ______lb.
We are 99.7% sure that the baby will be born
between _____lb and _____lb.
What is the likelihood that the baby will be less than
8.9 lbs?
Side 1 of Practice
Sheet
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Complete the first side of the
practice sheet:
Using the 68-95-99.7 Rule
Example 1(on 68-95-99.7)
The SAT test as 3 parts:
Writing, Mth, and Critical
Reading. Each part has a
distribution that is roughly
unimodal and symmetric,
an overall mean of 500
and a standard deviation
of 100 for all test takers.
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Suppose you earned a 600 on one part of the
SAT. Where do you stand among all students
who took the test?
1. Find Z score (600-500)/100 = 1
1. What percent is to the LEFT??
68% + ½(32%)= 84%
84th PERCENTILE
Percentiles
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What percentile are the following?
Example 2
(not on 68-95-99.7)
What if it is not EXACTLY 0, 1, 2, or 3
standard deviations away from mean?
• (what if z-score≠0,1,2,or 3)
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Suppose you earned a 680 on one part of the
SAT. Where do you stand among all students
who took the test? [N(500, 100)]
1. Find Z score (680-500)/100 = 1.8
1. What percent is to the LEFT??
WE HAVE A CHART FOR THAT
Second side of
Practice Sheet
Homework
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Ch. 6 #1, 17, 18, 23, 29, 30