## Question 421:

1## Answer:

No answer provided yet.We will use the binomial distribution properties to solve these questions.

- The binomial distribution is BIN(8,.80).
- The mean is NP or 8*.80 = 6.4
- The variance is NPQ, where Q is 1-P (.20). So the variance = 1.28
- You can use the Excel formula, =BINOMDIST(6,8,0.8,FALSE) where the parameters are the value of interest (6), the total trials (8), p (.8) and the logical paramater of False means to use the Probability Mass Function (PMF) which equals the exact probability for just 6. You should get .293601
- Use the same excel formula and change it to =BINOMDIST(5,8,0.8,TRUE) which computes the Cumulative Probability (adding up all probabilities up to 5/8 inclusive), you should get .20308, or the probability of successful surgery for less than 6 patients is a bit more than 20%.