Download Probablity Distribution (non specific)

Types of Distributions
Probablity Distribution (non specific)
o
o
Binomial Distribution

Probablities must add to 1
Expected Outcome (Mean of the distribution)—This
has been on every AP exam I have seen, either on
FRQ or MC
o
bg
 x   xi pi
B n, p

o
Multiply each outcome by its
probability and add together
Standard deviation (never been on AP exam that I
know of)
o
b

g
 x   xi   x pi
2

0
0.4
1
0.3
2
0.2
3
0.1
 x  (0)(0.4)  (1)(0.3)  2(0.2)  3(01
. )  10
.
On average, Landry’s sells 1 hat per week. He should buy
fifty two hats per year.
Normal Distribution

If there is reason to believe that a distribution is
normal, you must state that it is normal and state the
average (  ) and the standard deviation (  )
o
This can be done by simply writing the
shorthand version:

You must draw a normal curve picture with the
problem’s numbers referenced in it, and it would also
be good to reference the formula for a standardized
score (z-score)
o


b g
N , 
x
x
or z 
z

/ n
Calculate your probability, and verify with a
calculator
State your probability and its meaning in the context
of the question
Example: A box of candy is known to have an average of 50
pieces. If it is known that the amount of packaged candy is
normally distributed with a standard deviation of 5, is it likely
to get a box with 62 pieces?
b g z  62 5 50
Pb
X  62g
 Pb
z  2.4g
 0.0082
N 50,5

There is a 0.82% chance that a box would get 62 pieces of
candy or more. So this is very unlikely.

. Make sure to state what p
represents.
You must show that it meets the four criteria
o Success/Failure
o There are a set number (n) of observations
o Probability of success never changes
o Each observation is independent
Plug into the formula
o
Example: The number of hats sold at Landry’s per week is as
follows
X
P(X)
You must state that it is binomial, state what a
success is, what the probability of success is and how
many observations are being made.
o This can be done with the shorthand:
b g
b g
P X  k  n Ck  pk  1  p
n k
Describe you answer in the context of the question
Example: The probability of making any money in a state
lottery is 0.4. There is a drawing once a week. What is the
probably that you would win at least six times in a seven week
period?
B(7, 0.4) where n is the number of weeks being observed and
p = the probability of making any money = 0.4
1. success=making money/failure=not making money
2. There are seven weeks of observations
3. p = probability of winning = 0.4
4. There is no reason to believe that each drawing is not
independent
b g
 Pb
X  6g
 Pb
X  7g
Cb
0.4gb
0.6g C b
0.4gb
0.6g
P X6
6
7
1
6
7
7
0
7
 0.0172  0.0016
 0.0188
Geometric Distribution

1.
2.
3.
4.
Everything is the same as for a binomial, except for
rule #2
Same
Observations are made until a success occurs
Same
Same

Plug into formula
o
o
b g b g p
Pb
X  kg
b
1  pg
P X  k  1 p
k 1
k
Example: Using the information about the lottery above.
What is the probability that you would have to play at least 10
weeks until you got a win?
b g b gb g
P X  10  P X  9  0.6  0.01
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