To find the probability that at least 175 homes are going to be used as investment property, we can use the normal approximation to the binomial distribution.
First, let's find the mean and the standard deviation for the binomial distribution.
Mean (μ) = n * p
Standard Deviation (σ) = √(n * p * (1 - p))
Where n is the sample size (800) and p is the proportion of investment properties (0.23).
Mean (μ) = 800 * 0.23 = 184
Standard Deviation (σ) = √(800 * 0.23 * (1 - 0.23)) = √(147.92) = 12.16
Now, we will find the z-score for the given value (175).
z = (x - μ) / σ
z = (175 - 184) / 12.16 = -9 / 12.16 = -0.74
Using a standard normal distribution table or a calculator, we find the probability of a z-score less than -0.74 to be about 0.2295.
Since we need the probability of at least 175 homes, i.e., 1 minus the probability of less than 175 homes, we have:
Probability (at least 175 homes) = 1 - 0.2295 = 0.7705
So, the probability that at least 175 homes are going to be used as an investment property is approximately 0.7705 or 77.05%.
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 home are going to be used as investment property?
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