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BinomialProblems
2/10/2010
Binomial Problems from The Statistics Problem Solver
For each of these problems:
Plan
State your question
Verify that the conditions for the Binomial distribution are met
Define the random variable (x) you are interested in
determine what is
n
,
p
and
q
for the random variable
Show
do the mechanics of the problem using your TI83
Tell
State your conclusion based on your results.
Your conclusion must
be in the context of the problem
1.
Monty Python completed 60% of his passes one season.
Assuming he stays
healthy and maintains his record as a quarterback, what is the probability that
he will complete 80 of his first 100 passes in the next season?
n = _100
_
p = _0.6
_
q = _0.4
_
x = __80
_
This problem satisfies the conditions for a Binomial.
1.
There are a fixed number of trials
–
throwing a pass.
Each pass is independent of
the other passes.
2.
There are only 2 possible outcomes:
successfully completing a pass or failure which
is an incomplete pass.
3.
The probability of completing a pass stays the same for each trial.
4.
The random variable counts the number of complete passes.
Using your TI83, go to Dist like your text book says and use:
Binompdf(100,.6,80) which
will give you 1.053 x 10
5
or 0.00001053
This means that if everything stays the same, the chance of Monty completing 80 passes is
very remote.
His average is
np
or 60 per 100 so this makes sense.
2.
There are 20 machines on the plant floor of a local manufacturing company.
Due to uptime problems, the probability that a machine is working at the end of
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 Winter '10
 C.Eckerle
 Math, Statistics, Binomial, Probability, Probability theory, Monty Python, Discrete probability distribution

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