Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372
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The Binomial
37.2
Distribution
Introduction
A situation in which an experiment (or trial) is repeated a fixed number of times can be modelled,
under certain assumptions, by the binomial distribution. Within each trial we focus attention on
a particular outcome. If the outcome occurs we label this as a success. The binomial distribution
allows us to calculate the probability of observing a certain number of successes in a given number
of trials.
You should note that the term ‘success’ (and by implication ‘failure’) are simply labels and as such
might be misleading. For example counting the number of defective items produced by a machine
might be thought of as counting successes if you are looking for defective items! Trials with two
possible outcomes are often used as the building blocks of random experiments and can be useful to
engineers. Two examples are:
1. A particular mobile phone link is known to transmit 6% of ‘bits’ of information in error. As an
engineer you might need to know the probability that two bits out of the next ten transmitted
are in error.
2. A machine is known to produce, on average, 2% defective components. As an engineer you
might need to know the probability that 3 items are defective in the next 20 produced.
The binomial distribution will help you to answer such questions.
Prerequisites
understand the concepts of probability
Before starting this Section you should . . .
recognise and use the formula for
binomial probabilities
Learning Outcomes
state the assumptions on which the binomial
On completion you should be able to . . .
model is based
17
HELM (2008):
Section 37.2: The Binomial Distribution
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