Need statistics help with The success rate of a corneal transplant surgery is 80%.

Statistics
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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.

Dec 1st, 2015

Thank you for the opportunity to help you with your question!

Thanks Gabbi for more questions!

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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 1st, 2015

Thank you so much u are a great help! Do you mind answering a few more for me? My test is due tomorrow and I'm SO stuck on these questions :(

Dec 1st, 2015

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