Question

Suppose you intend to draw a sample of 100 residents from the large population of residents living in Blanchard County, Mississippi. You plan to compute the mean age (x) in the sample. The most recent Census shows that the average age of Blanchard County residents is 38 years, with a standard deviation of 12 years. Assuming that the Census figures still apply,
a. Sketch a graph of the sampling distribution that would assign probabilities to the various values that your sample mean computation could produce.
b. What is the probability that your sample mean will have a value somewhere between 37 and 39?
c. It is 80% likely that the sample mean you compute will be somewhere between ____ and ____ years. (Make your interval symmetric around the population mean.)
d. What is the probability that the sample mean you compute will be within 1.96 standard deviations (that is, ±1.96σx) of the mean age of the Blanchard County population?

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