Question

According to the website www.olx.uz, monthly rent for a two-bedroom apartment has a mean of

Answer 1

Using the normal distribution and the central limit theorem, it is found that there is a 0.0571 = 5.71% probability of selecting a sample  of 40 two-bedroom apartments and finding the mean to be at least $275 per month.

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

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

• It 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, which is the percentile of X.

In this problem:

• The mean is of $250, hence $\mu = 250$.

• The standard deviation is of $100, hence $\sigma = 100$.

• The sample is of 40 apartments, hence $n = 40, s = \frac{100}{\sqrt{40}}$.

The probability of selecting a sample  of 40 two-bedroom apartments and finding the mean to be at least $275 per month is the p-value of Z when X = 275, hence:

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

By the Central Limit Theorem

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

$Z = \frac{275 - 250}{\frac{100}{\sqrt{40}}}$

$Z = 1.58$

$Z = 1.58$ has a p-value of 0.9429.

1 - 0.9429 = 0.0571

0.0571 = 5.71% probability of selecting a sample  of 40 two-bedroom apartments and finding the mean to be at least $275 per month.

You can learn more about the normal distribution and the central limit theorem at brainly.com/question/24663213