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 most200 homes are going to be used as investment property?
A) 0.9099
B) 0.4066
C) 0.0934
D) 0.5935

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution or normal approximation to the binomial distribution. Given the large sample size (n = 800) and a probability of success (p = 0.23), the normal approximation is suitable. The mean (μ) of the distribution is np = 800 * 0.23 = 184, and the standard deviation (σ) is sqrt(np(1-p)) = sqrt(800*0.23*0.77) ≈ 12.96. To find the probability of at most 200 homes, we convert this to a Z-score and look up the value in a standard normal distribution table or use a calculator. The Z-score for 200 is (200-184)/12.96 ≈ 1.23. Looking up the Z-score of 1.23 in the standard normal distribution table or using a calculator gives us a probability of approximately 0.9099. This means there's about a 90.99% chance that at most 200 homes out of the sample will be used as investment property.

The National Association of Realtors Estimates That 23% of All