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Transcript
 X  p1 x1  p2 x2  p3 x3 
 X   pi xi
AP Statistics, Section 7.2, Part 1
 pn xn
2
 The
Michigan Daily Game you pick a 3 digit
number and win \$500 if your number
matches the number drawn.
 What

is the average winnings?
1st we need to know, For a 3 digit number how
many ways can you win?
 10 X 10 X 10 = 1000 combinations of 3 digit #s
 so, 1/1000 or .001
chance of winning
 X  .001(500)  .999  0 
 .50  0
Is this a fair
game?
 .50
AP Statistics, Section 7.2, Part 1
3

The Michigan Daily Game
you pick a 3 digit number
and win \$500 if your
number matches the
number drawn. If it cost
\$1.00 to play.
 X  .001(499)  .999  1
 .499  .999
 .50
What is the average
PROFIT?
-.50
Mean = Expected Value

AP Statistics, Section 7.2, Part 1
4
  p1  x1   x   p2  x2   x  
2
X
2
   pi  xi   x 
2
X
AP Statistics, Section 7.2, Part 1
 pn  xn   x 
2
2
5
2
 The
Michigan Daily
Game you pick a 3
digit number and win
matches the number
drawn.
 What
is the average
winnings?
  (500  .5)  .001
2
X
2
  0  .5   .999
2
 249.50025  .24975
 249.75
  15.8
Standard dev. / Variance is how much difference there is in the
measurements.
AP Statistics, Section 7.2, Part 1
6
 Draw
independent observations at random
from any population with finite mean μ.
 Decide
how accurately you would like to
estimate μ.
 As
the number of observations drawn
increases, the mean x-bar of the observed
values eventually approaches the mean μ
of the population as closely as you
specified and then stays that close.
AP Statistics, Section 7.2, Part 1
7
 The
distribution of the heights of all young
women is close to the normal distribution
with mean 64.5 inches and standard
deviation 2.5 inches.
 What
happens if you make larger and larger
samples…
AP Statistics, Section 7.2, Part 1
8
AP Statistics, Section 7.2, Part 1
9
 Most
people incorrectly believe in the law of
small numbers.
 “Runs”
of numbers, etc.
AP Statistics, Section 7.2, Part 1
10
 Exercises:
7.13-7.33 odd x21
AP Statistics, Section 7.2, Part 1
11