The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most
200 homes are going to be used as investment property?
A) 0.9099
B) 0.4066
C) 0.0934
D) 0.5935

Question

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most
200 homes are going to be used as investment property?
A) 0.9099 
B) 0.4066 
C) 0.0934 
D) 0.5935

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution or normal approximation to the binomial distribution. Given p = 0.23 (probability of a home being an investment property), n = 800 (sample size), and we're looking for the probability of x ≤ 200. Using normal approximation (since np and n(1-p) are both greater than 5), we find the z-score and then the cumulative probability up to that z-score. The closest match to the calculated probability using the normal approximation method is 0.9099, making option A the correct choice.

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