Oglethorpe University

BIOSTAT 111

Problem Set 6
7.1. 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?
Nominal variable with two discrete outcomes (resistant or not resistant)
Comparison b/w null proportion (po = 30% = 0.30) and measured proportion (phat = 5/7 = 0.71)
--Yes, binomial test is applicable
b. Using the binomial distribution, what is the probability of success for this example? What is n?
n = 7 (total number of independent isolates)
probability of success = 0.7143
c. Calculate the probability of exactly five resistant isolates using the binomial distribution.
Pr[successes = 5] = 0.0250
d. Calculate the probability of exactly six resistant isolates, and calculate the probability of
exactly seven resistant isolates.
Pr[successes = 6] = 0.0036
Pr[successes = 7] = 0.0002
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.
0.025 + 0.0036 + 0.0002 = 0.0288
8.2. The parasitic nematode Camallanus oxycephalus infects many freshwater fish, including shad. The
following table gives the number of nematodes per fish (Shaw et al. 1998):