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put this solution on YOUR website!In a recent survey, 66% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the police substation.
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This is a binomial probability problem.
The formula for that is:
for x=0,1,2,...,n
Where:
n=number of trials
x=number of successes among n trials
p=probability of success in any one trial
q=probability of failure in any one trial (q=1-p)
:
! is a factorial symbol that denotes the product of descending numbers, like this:
4!=4*3*2*1 If your in a statistics class you probably have a calculator with the ! symbol available some where. For the TI 83 to TI 84, hit [MATH] arrow right>>> to PRB it's 4:!.
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Some teachers allow you to shorten the formula to:
P(x)=[n]C[r]*p^x*q^(n-x)
r=x=number of successes among n trials.
All of the other symbols are the same as the first formula. If you're one of those, then you should know how to do it with your calculator.
:
I'm going to show you with the first formula.
p=66/100=.66
q=1-p=1-.66=.34
n=14
x=11
Round to whatever your teacher wants, most don't require more than 4 decimal spots.
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I don't know how much work your teacher needs to see. If they only want an answer, then....
If you have a TI 83 to TI 84, these can be done by following these steps:
[2nd] [VARS] arrow down to 0:binompdf [ENTER]
type in [n] [,] [p] [,] [x] [)] [ENTER]
In this case it will look like binompdf(14,.66,11)=.1480885312
:
Look the instructions up for the calculator that you're using if it's not a TI 83 or 84.
Happy Calculating!!!!
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