Shirley Johnson, a county political leader, is looking ahead to next year’s elec

Question

Shirley Johnson, a county political leader, is looking ahead to next year’s election campaign and the possibility that she might be forced to support a property tax increase to help combat projected shortfalls in the county budget. For the dual purpose of gaining voter support and finding out more about what her constituents think about taxes and other important issues, she is planning to hold a town meeting with a simple random sample of 40 homeowners from her county. For the more than 100,000 homes in Shirley’s county, the mean value is $190,000 and the standard deviation is $50,000. What is the probability that the mean value of the homes owned by those invited to her meeting will be greater than $200,000?

Explanation / Answer

Since the standard deviation of the sampling distribution of the means is the population standard deviation divided by the square of sample size, which in this case would be 50,000 divided by the square root of 40,

The z score is (200,000-190,000)/(50,000/square root of 40) = 1.2649

P(mean > 200,000) = P(Z>1.2649) = 1 - normalcdf(-1E99,1.2649,0,1) = 1 - 0.8970 = .1030

answer: .1030

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