Artie Fact wants to determine the total value of all of the houses in his city. So he goes to the tax Assessor's Office and looks up the value of 30 houses in the city. He finds that the averages of these houses is about $87,300 houses , with a standard deviation of $5,400. From the tax rolls he finds that there are 7468 within the city limits. So he concludes that the total value of the houses is about 652 million dollars. Is this a reasonable estimate? Use the Central Limit Theorem to determine your answer.

Question

Artie Fact wants to determine the total value of all of the houses  in his city. So he goes to the tax Assessor's Office and looks up the value of 30 houses in the city. He finds that the averages of these houses is about $87,300 houses , with a standard deviation of $5,400. From the tax rolls he finds that there are 7468 within the city limits. So he concludes that the total value of the houses is about 652 million dollars. Is this a reasonable estimate? Use the Central Limit Theorem to determine your answer.