Survey of health problems. A survey selects an SRS of n = 500 people from a town

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Survey of health problems. A survey selects an SRS of n = 500 people from a town of 55,000. The sample shows a mean of 2.30 health problems per person (standard deviation = 1.65). Based on this information, say whether each of the following statements is true or false. Explain your reasoning in each instance.

(a) The standard deviation of the sample mean is 0.074.

(b) It is reasonable to assume that the number of health problems per person will vary according to a Normal distribution.

(c) It is reasonable to assume that the sampling distribution of the mean will vary according to a Normal distribution.

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