BES Tutorial Sample Solutions, S1/10
WEEK 6 TUTORIAL EXERCISES (To be discussed in the week starting
April 12)
1.
Among employed women, 25% have never been married. Select 12
employed women at random.
(a)
The number in your sample who have never been married has a
binomial distribution. What are the binomial parameters
n
and
p
?
n=12, p=.25
(b)
What is the probability that exactly 2 of the 12 women in your sample
have never been married?
ܲሺܺ ൌ 2ሻ ൌ
12!
2! 10!
0.25
ଶ
ሺ1 െ 0.25ሻ
ଵ
ൌ 0.2323
(c)
What is the probability that 2 or fewer have never been married?
ܲሺܺ 2ሻ ൌ ܲሺܺ ൌ 0ሻ ܲሺܺ ൌ 1ሻ ܲሺܺ ൌ 2ሻ ൌ 0.0317 0.1267 0.2323
ൌ 0.3907
2.
A telemarketer is employed to telephone 10 households each evening
between 6 and 7pm with a view to selling a particular service.
From past
experience it is known that the probability of any one household being
interested in purchasing the service is
p
= 0.20.
Let the random variable
X
represent the number of households called on a given evening that are
interested in the service.
(a)
Comment on the suitability of modelling the (relative frequency)
distribution of
X
as a binomial distribution.
Recall that we can summarize the precise requirements for a binomial
experiment as follows:
There are n identical and independent trials.
There are only two possible outcomes for each trial: success and failure.
The probability of a success p is the same for each trial.
Is it reasonable to suppose our example satisfies all these conditions?
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Independence is often the most problematic assumption but if we’re
drawing from a large market it seems a reasonable assumption here.
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 Three '11
 DenzilGFiebig

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