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Question 353:



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  1. The binomial distribution is BIN(8,.80).
  2. The mean is NP or 8*.80 = 6.4
  3. The variance is NPQ, where Q is 1-P (.20). So the variance = 1.28
  4. 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
  5. 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%. 

See also question 325

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