Description
The success rate of corneal transplant surgery is 80%. The surgery is performed on six patients.
(1) Find the mean, variance, and the standard deviation of the probability distribution.
(2) Find the probability that the surgery is successful for exactly three patients.
(3) Find the probability that the surgery is successful for fewer than four patients.
Explanation & Answer
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1) This question again follows Binomial distribution.Given n=6 p=80% = 0.8
q= 1-p = 0.2
Mean l = np = 6*0.8 = 4.8
Variance = npq = 6*0.8*0.2 = 0.96
Standard Deviation = Sqrt(Variance) = 0.9797
2) P(exactly three) = P(X=3) = (e^-l) * (l^x)/x! = {(e^-4.8)*(4.8^3)}/3! = 18.43*0.0082 = 0.1516
3) P(fewer than 4) = P(X=0)+P(X=1)+P(X=2)+P(X=3) = (e^-4.8)(1+4.8+(4.8^2)/2 +(4.8^3)/6)
= 0.0082(18.43+11.52+5.8) = 0.2931
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