Calculation practice: Binomial probabilities. Enterococcus bacteria are part of the normal intestinal flora of humans, but some strains can cause disease. In U.S. hospitals, 30% of pathogenic isolates are resistant to the antibiotic vancomycin (Wenzel 2004). Assume that seven independent pathogenic isolates have been extracted from patients and tested for resistance. Using the following steps, calculate the probability that five or more of the isolates are resistant to vancomycin:

a. What are the assumptions of the binomial distribution? Does this example match those assumptions?

b. Using the binomial distribution, what is the probability of success for this example? What is

c. Calculate the probability of exactly five resistant isolates using the binomial distribution.

d. Calculate the probability of exactly six resistant isolates, and calculate the probability of exactly seven resistant isolates.

e. Using the addition principle, combine the information from the previous answers to calculate the probability of five or more resistant isolates out of seven.

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