Question

A new surgical procedure is said to be successful 80% of the time. Suppose the procedure is performed 5 times and the results are assume to be independent of one another. What are the following probabilities?

A. All 5 of the procedures are successful?
B. Two or less are successful?
C. What is the mean (or expected) number of successful procedures?
D. What is the standard deviation of successful procedures?

Answer 1

Let X be a new surgical procedure

So X follow Binomial ( n=5 , p=0.80)

A)

P(X=5) =

=

= 0.3276

B) =  P(X=0) + P(X=1) + P(X=2)

= +   +  

= 0.00032 + 0.0064 + 0.0512

= 0.05792

C) mean = n*p

= 5*0.8

mean = 4

D) Standard deviation = (n*p*q)^1/2

= (5*0.8*0.2)^1/2

= 0.8944