SOLUTION: In a given year, 24% of the people in a community use the emergency room at the local hospital. A random sample of 26 people is selected. A researcher wishes to know the pr

Question 1116664: In a given year, 24% of the people in a community use the emergency room at the local hospital.
A random sample of 26 people is selected.
A researcher wishes to know the probability that a fixed number of individuals in the sample will have used the emergeny room in the last year.

a) Explain why this situation will involve a binomial probability distribution.

b) Find the probability that in a sample of 26, exactly 9 people used the emergency room.

c) Find the probability that in a sample of 26, 9 or fewer people used the emergency room.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a given year, 24% of the people in a community use the emergency room at the local hospital.
A random sample of 26 people is selected.
A researcher wishes to know the probability that a fixed number of individuals in the sample will have used the emergeny room in the last year.
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a) Explain why this situation will involve a binomial probability distribution.
An "event" is the selection of a person.
The event results are independent.
Prob of "success" for each event is the same,0.24
Each event is either a success or a failure.
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b) Find the probability that in a sample of 26, exactly 9 people used the emergency room.
P(x = 9) = 26C9*0.24^9*0.76^17 = binompdf(26,0.24,9) = 0.0777
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c) Find the probability that in a sample of 26, 9 or fewer people used the emergency room.
P(0<= x <=9) = binomcdf(26,0.24,9) = 0.9279
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Cheers,
Stan H.
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