SOLUTION: 10 people get a flu shot which has an 80% chance of preventing the flu: What is: 1) probability shot prevents all 10 people from getting the flu. 2) probability at least 8 peopl

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Question 764067: 10 people get a flu shot which has an 80% chance of preventing the flu:
What is:
1) probability shot prevents all 10 people from getting the flu.
2) probability at least 8 people are prevented from getting the flu.
3) calculate the expected value and standard deviation of number of people prevented from getting the flu. Please show formulas! :)

Found 2 solutions by stanbon, reviewermath:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
10 people get a flu shot which has an 80% chance of preventing the flu:
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Binomial Problem with n = 10 and p(prevent) = 0.8
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What is:
1) probability shot prevents all 10 people from getting the flu.
P(x=10) = 10C10*0.8^10*0.2^0 = 0.8^10 = 0.1074
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2) probability at least 8 people are prevented from getting the flu.
P(8<=x<=10) = 1 - P(0<=x<=7) = 1-binomcdf(10,0.8,7) = 0.6778
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3) calculate the expected value and standard deviation of number of people
prevented from getting the flu.
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mean = np = 10*0.8 = 8
std = sqrt(npq) = sqrt(8*0.2) = sqrt(1.6) = 1.2649
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Cheers,
Stan H.
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Please show formulas! :)

Answer by reviewermath(1029) (Show Source):
You can put this solution on YOUR website!
10 people get a flu shot which has an 80% chance of preventing the flu:
What is:
1) probability shot prevents all 10 people from getting the flu.
=
2) probability at least 8 people are prevented from getting the flu.
=
3) calculate the expected value and standard deviation of number of people prevented from getting the flu.
Expected Value = np = 10(0.8) =
Standard Deviation = = =