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Calculating mean and standard deviation for a sample from a binomial distribution.

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Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that of its customers order their food to go. Suppose that this proportion is correct and that a RANDOM SAMPLE of 40 individual customers is taken.

a. Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

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the following solution uses a binomial distribution to calculate the mean of a sample and the standard deviation.

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