11 , A certain surgical procedure has an 85% chance of success. A doctor perform

Question

11 , A certain surgical procedure has an 85% chance of success. A doctor performs the procedure on fifteen patients. Find a. The mean of the procedure b. The standard deviation c. Find the probability of the surgery being successful on exactly five patients d. Find the probbility of the surgery being successful on less than four patients e. Find the probability of the surgery being successful between 9 and 13 patients inclusive f. Find the probability of the surgery being successful on more than 7 patients g. Find the probability of the surgery being successful on at least 1 patient MacBook Air 888, 8 7 8 9 6 5

Explanation / Answer

Solution:- Given that n = 15 , p = 0.85 , q = 0.15

a. mean = n*p = 15*0.85 = 12.75

b. standard deviation : sqrt(n*p*q) = sqrt(15*0.85*0.15) = 1.3829

c. P(X = 5) = 0.0000076

d. P(X < 4) = < 0.000001 (or) 0.0000

e. P(9 <= X <= 13) = P(9)+P(10)+P(11)+P(12)+P(13)
= 0.0132+0.0449+0.1156+0.2184+0.2856
= 0.6777

f. P(X 1) = 0.999999

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