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Tut sol week6 - BES Tutorial Sample Solutions S1/10 WEEK 6...

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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 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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