The National association of Realtors estimates that 23% of all homes purchased i
ID: 3362415 • Letter: T
Question
The National association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most 25% of the homes are going to be used as investment property? Would like this problem to be solved with a calculator TI-84 The National association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most 25% of the homes are going to be used as investment property? Would like this problem to be solved with a calculator TI-84Explanation / Answer
the population proportion (p) is 0.23 (23%/100 = 0.23).
Therefore, the mean of the sampling distribution is 0.23.
The sample size is 800, so the standard deviation is sqrt ((0.23(1-0.23))/800) = sqrt ((0.1771)/800) = 0.0149
calculate the z-score for the sample proportion 0.25 using the sampling distribution information.
z = (p-hat - mean) / std dev = (0.25 - 0.23) / 0.0149 = 1.34
The probability that "at most 200 homes are used" is the same as the probability that less than 200 homes are used.
This probability is the area to the left of 1.34. The area to the left of z = 1.34 is 0.9099.
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