Mathematics, 30.03.2021 08:20 student10190

5) The National Association of Realtors estimatest that 23% of all homes purchased in 2004 were considered investment properties. If a random sample of 800 homes sold in 2004 is obtained, what is the probability that al
most 25% of those are used as investment property?

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Answer from: coreybro

0.9099 = 90.99% probability that at most 25% of those are used as investment property.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

23% of all homes purchased in 2004 were considered investment properties.

This means that p = 0.23

Sample of 800 homes

This means that n = 800

Mean and Standard deviation:

$\mu = p = 0.23$

$\sigma = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{800}} = 0.0149$

What is the probability that at most 25% of those are used as investment property?

This is the pvalue of Z when X = 0.25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.25 - 0.23}{0.0149}$

Z = 1.34

Z = 1.34 has a pvalue of 0.9099

0.9099 = 90.99% probability that at most 25% of those are used as investment property.

Answer from: Quest

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

hope it will

#faazmessi

The answers to how the polygons are similar?

Answer from: Quest

the square root of what number? if you add that, then someone will probably answer the question.

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