SOLUTION: An archer is able to hit the bull's-eye 55% of the time. She will shoot 8 arrows. Let X = the number of arrows which hit the bulls - eye. a. For each of the requested probabilitie

Question 1114947: An archer is able to hit the bull's-eye 55% of the time. She will shoot 8 arrows. Let X = the number of arrows which hit the bulls - eye.
a. For each of the requested probabilities: express the probability in terms of X, and find the probability.
1. The probability that the archer hits the bulls - eye exactly 4 times.
2. The probability that she hits the bulls - eye no more than 5 times.
b. The mean of X is 4.4 arrows, but clearly, the archer cannot hit the target 4.4 times! please interpret this mean of X.
C. 1. Show a calculation which would giv the mean of X
2. Find the standard deviation of X.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
For 8 arrows
p(4)=8C4*(0.55^4)(0.45)^4
=70*0.0915*0.0410=0.0458
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no more than 5
do 6,7,8 and subtract from 1
8 is 0.45^8=0.0017
7 is 8C7*0.55*0.45^7=0.0164
6 is 8C6*0.55^2*0.45^6=0.0703
Those 3 add to 0.0884
Subtract from 1 and the answer is 0.916 probability.
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The expected value is 4.4, which means if this is performed an infinite number of times, the average will be 4.4
The E(X)=x*p(x)=8*0.55=4.4
V(X)=np(1-p)=4.4*0.45=1.98
SD is sqrt (V(X))=1.41

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