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hw5solu_STAT515Fall2011

# hw5solu_STAT515Fall2011 - Solution to Homework 5(STAT515...

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Solution to Homework 5 (STAT515, Fall 2011) 4.60. ( 20 points ) a. ( 5 points ) One needs to assume that the sample of five brands forms an independent sample from a big population of bottled-water brands. Then one can view the experiment, “inspecting these five brands to see if they use tap water”, as an experiment that consists of 5 independent trials. Clearly, the outcome of each trial is either “Yes, this brand uses tap water.” or “No, this brand does not use tap water.” That is, the outcomes of each trial (for each bottle) is dichotomized, like “success” and “failure” in an binomial experiment. Moreover, if it is known that 25% of the population use tap water, then for each trial the probability of “success” is 0.25. Now that this experiment has all the characteristics of a binomial experiment, the random variable, X = the number of brands among the five selected that use tap water, is a binomial random variable.

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