Enterococcus bacteria are part of the normal intestinal flora of humans, but som

Question

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 nine independent pathogenic isolates have been extracted from patients and tested for resistance. Using the following steps, calculate the probability that six or more of the isolates are resistant to vancomycin.

Does this example match the assumptions of a binomial distribution (yes or no)?

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

What is n?

Explanation / Answer

Assumptions of binomial distribution

1) The number of trials n is fixed , here n = 9

2) The probability of outcome is same across n trials , here p = 0.30

3) Trials are independent.

So assumptions of binomial distribution match here.

We can use binomial probability distribution

p(x) = nCx px (1-p)n-x

P( x >= 6) = p(x = 6) + p( x = 7 ) + p( x =8) + p (x = 9)

= 9C6 0.306 0.703 + 9C7 0.307 0.702 + 9C8 0.308 0.701 + 9C9 0.309 0.700

= 0.0253

P( x >= 6) = 0.0253

n = 9.

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