Transcript Notes on Determining Normality and using the Calculator

2.2 Determining and Using
Normal Distributions
So, what if you have got some
data…
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And, you want to know if it is
essentially normally distributed…
1. WHY WOULD WE WANT TO KNOW
THAT??
 Because if it is, then we can approximate
proportions between values using the
normal table or normal calculator function!
2. Okay, maybe that might be useful. So
how do we decide?
Normal Probability Plot!!
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What?
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A plot made by looking at how data points are spread out…
do they pretty much follow the 68-95-99.7 rule?
If so, your Normal Probability Plot should look linear.
If not approximately normally distributed it won’t look linear.
How?
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Enter data in L1
In StatPlot choose the very last picture– the one that looks
like a line, tell it where your data is stored (ie L1), choose ‘X’
and any mark you would like.
Graph with ZoomStat.
Deciding on normality…
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Best way- Normality Plot
OTHER WAYS TO HELP SUPPORT NORMALITY:
 See if it follows the 68-95-99.7 rule using the
standard deviation and the mean
 Look at the data to see if it is roughly
symmetric (box plot, histogram)
 Are the mean and median about the same?
To find normal areas using
calculator:
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Press 2nd VARS (DISTR)
Choose the 2nd option
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Complete the command
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normalcdf(
normalcdf(lower x, upper x, , ) or
normalcdf(lower z, upper z)
For infinity, use 1EE99
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EE is above the comma. To type EE, type
2nd comma
Using the Calculator instead of
table A.
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Find the proportions of observations
from standard normal distributions for
z 2.5
 Find the proportions of observations
below 20 given N(15,2)
 WHY ARE THEY THE SAME????
To find normal proportions given
observed variable:
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State problem, draw sketch.
Standardize x using z =(x-)/.
Use the table. (Note if you are finding area to left or area to
right.)
OR
 Use the calculator NormCfd(lower z , upper z) = area
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Write conclusion in context of problem.
A z-score outside the range of table A can be
considered essentially 0 since the area of the last
entry is .002. Anything beyond that will continue to
decrease and is insignificant BUT NOT ZERO (close to
zero, essentially zero, but not equal to zero).
SHOW YOUR WORK!!
Let’s try one together! #1
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According to the children’s growth chart
that doctors use as a reference, the
heights of two-year-old boys is normally
distributed with a mean of 34.5 inches
and a standard deviation of 1.3 inches.
If a two year old boy is selected at
random, what is the probability that he
will be between 32.5 and 36.5 inches
tall?
Answer:
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Draw distribution and shade.
Show calculation. If you use the
Calculator show what you entered.
Write an final sentence.
EX: Distribution on the board.
Normcdf(32.5, 36.5, 34.5, 1.3)= .8764
There is an 88% chance that a 2 yearold boy will be between the height of
32.5 and 36.5 inches.
To find x-value given normal
proportion
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State problem, draw sketch.
Use table. (Locate entry closest to given % and
find corresponding z-score.)
OR
 Use Calculator Function InvNorm(% written as a
decimal) = z score
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Un-standardize the value using z =(x-)/.
Write conclusion in context of problem.
SHOW YOUR WORK!!
InvNorm(%/100) = z!!
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Type 2nd Vars
Go to 3: InvNorm(
Type in the percentile (% below) as a
decimal
This is the z-score associated with this
percentile.
Let’s try another! #2
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According to government reports the
heights of adult male residents in the
US is approximately normal
distributed with a mean of 69.0
inches and a standard deviation of
2.8 inches. If a clothing
manufacturer wants to limit his
market to the central 80% of adult
males, what range of heights should
be targeted?
Answer:
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Draw distribution and shade. Determine the percent
of the part you want.
Show calculation. If you use the Calculator show
what you entered.
Write an final sentence.
EX: Distribution on the board.
We want to find the z-scores associated with z<a=.1
and z<b=.9. Use the tables or Calculator to find the
z-scores. a=-1.28 and b=1.28.
Un-standardize the value using z =(x-)/
80% of the male population are between the
heights of 72.6 and 65.4 inches.
HW:
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DO # 30, 31, 33, 35, 38, 40, 44, 45, 47,
49
Show all calculations and make sure
you write you answers contextually with
meaning.
Test on Fri 9/17 and Mon 9/20
Fill in toolkit.