Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372 Page 13
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Answer
Consider the occurrence of a six, with X being the number of sixes thrown in 36 trials.
The random variable X follows a binomial distribution. (Why? Refer to page 18 for the criteria
if necessary). A trial is the operation of throwing a die. A success is the occurrence of a 6 on a
1
1
particular trial, so p =
. We have n = 36, p =
so that
6
6
1
1
5
E(X) = np = 36
= 6
and
V (X) = npq = 36
= 5.
6
6
6
Hence the standard deviation is σ =
5
2.236.
E(X) = 6 implies that in 36 throws of a fair die we would expect, on average, to see 6 sixes. This
makes perfect sense, of course.
29
HELM (2008):
Section 37.2: The Binomial Distribution
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