Compute Probabilities of a Sample Proportion
-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 least 175 homes are going to be used as investment property?
A) $0.7764$
B) $0.4821$
C) $0.2236$
D) $0.5189$

Question

Quizplus · Accepted Answer

The probability of at least 175 homes being used as investment property can be found using the normal approximation to the binomial distribution. The mean ($\mu$) of the distribution is $np = 800 \times 0.23 = 184$ and the standard deviation ($\sigma$) is $\sqrt{np(1-p)} = \sqrt{800 \times 0.23 \times 0.77} \approx 12.96$. To find the probability of at least 175 homes, we calculate the Z-score for 174.5 (for continuity correction) and find the probability to the right of this Z-score. The Z-score is $(174.5 - 184) / 12.96 \approx -0.733$. Looking up this Z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.7764.

Compute Probabilities of a Sample Proportion -The National Association of Realtors

Compute Probabilities of a Sample Proportion
-The National Association of Realtors