Lesson 11 Review of Calculator Functions - math-b
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Transcript Lesson 11 Review of Calculator Functions - math-b
SAT/ACT
ACT Summary Stats:
Max SAT: 1600 (old
school)
Max ACT: 36
SAT = 40 x ACT + 150
Lowest = 19
Mean = 27
SD = 3
Q3 = 30
Median = 28
IQR = 6
Find equivalent SAT
scores
ACT Summary Stats:
𝐿𝑜𝑤𝑒𝑠𝑡𝑆𝐴𝑇 = 40 ∗ 19 + 150
= 910
Lowest = 19
Mean = 27
SD = 3
Q3 = 30
Median = 28
IQR = 6
𝑀𝑒𝑎𝑛𝑆𝐴𝑇 = 40 ∗ 27 + 150
= 1,230
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑆𝐴𝑇 = 40 ∗ 3
= 120
𝑄3𝑆𝐴𝑇 = 40 ∗ 30 + 150 = 1,350
𝑀𝑒𝑑𝑖𝑎𝑛𝑆𝐴𝑇 = 40 ∗ 28 + 150
= 1,270
𝐼𝑄𝑅𝑆𝐴𝑇 = 40 ∗ 6 = 240
SAT = 40 x ACT + 150
The NormalCDF(
function finds the
percent of the total
area of the distribution
that falls between two
z-scores.
For example, what
would the
NormalCDF(-1,1) be?
(Hint: 68-95-99.7 rule)
First, determine the
type of question being
asked
Once you’ve
determined it is
appropriate to use the
NormalCDF function,
convert given values
into z-scores
𝑧=
𝑦−𝑦
𝑆𝐷
Questions:
Answers:
What percent of the
distribution falls
between X and Y?
NormalCDF(X,Y)
What percent of the
distribution is greater
than Y?
NormalCDF(Y,99)
What percent of the
distribution is less than
X?
NormalCDF(-99,X)
The invNormal( function
finds what z-score would
cut off that percent of the
data
The trick here is figuring
out what percent (as a
decimal) to enter in to the
function.
Example: What z-score cuts
off the top 10% in a Normal
model? The bottom 20%?
Imagine invNormal
calculates the area starting
at -99.
So to find the z-score that
cuts off the top 10% we
want the z-score that
includes 90%
invNormal (.9) = 1.28
Based on the model
N(1152, 84) describing
angus steer weights,
what are the cut-off
values for
A) highest 10%
B) lowest 20%
C) middle 40%
A) invNormal(.9) = 1.28
B) invNormal(.2) = -.842
C) invNormal(.3) = -.524
invNormal(.7) = .524
A)
B)
C)
1,259lbs
1,081lbs
1,108 – 1196lbs
How to decide when the
normal model (unimodal
and symmetric) is
appropriate:
Draw a picture
(Histogram)
Draw a picture! (Normal
Probability Plot)
A Normal Probability Plot
is a plot of Normal Scores
(z-scores) on the x-axis vs
the units you were
measuring on the y-axis
(weights, miles per
gallon, etc.)
A unimodal and
symmetric distribution
will create a straight line
A Normal probability
plot takes each data
value and plots it
against the z-score you
would expect that
point to have if the
distribution were
perfectly normal
These are best done on
a calculator or with
some other piece of
technology because it
can be tricky to find
what values to “expect”
Page 136-141
# 3, 5, 12, 17, 28, 30