6.1 Binomial Distribution

In many instances, microbiologists collect data that are binary. That is, data can occur in one of two possible outcomes, such as 0/1, +/–, growth/no growth, or pass/fail. The frequencies of each outcome are tabulated, relative to the number of trials, providing a data set ranging from 0 to 1.0. For example, let's take the number of trypticase soy broth tubes that are positive (+) for microbial growth over a 72-h incubation. Suppose ten tubes were used, and eight tubes were positive for growth. Then the proportion of positive growth is the number of positives ÷ total number = 8 ÷ 10 = 0.80. The value, “p,” is usually designated as the proportion of successes, in this case, positive (+) growth. The proportion of no-growth can also be calculated. The proportion of no-growth is q = 1 – p, or 1.0 – 0.80 = 0.20. Incidentally, what one terms “success” and “failure” is arbitrary.

There are many applications appropriate to using the binomial distribution, such as...


Decision Rule Peracetic Acid Standard Deviation Estimate Binomial Data Initial Spore 
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© Springer Science+Business Media, LLC 2008

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