
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”
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