## The mean rent of a 3-bedroom apartment in Orlando is $1300. You randomly select 10 apartments around town. The rents are normally distribute

Question

The mean rent of a 3-bedroom apartment in Orlando is $1300. You randomly select 10 apartments around town. The rents are normally distributed with a standard deviation of $350. What is the probability that the mean rent is more than $1100?

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2021-12-27T17:30:19+00:00
2021-12-27T17:30:19+00:00 1 Answer
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## Answers ( )

Answer:96.49% probability that the mean rent is more than $1100

Step-by-step explanation:To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distributionProblems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit TheoremThe Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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

In this problem, we have that:What is the probability that the mean rent is more than $1100?This is 1 subtracted by the pvalue of Z when X = 1100. So

By the Central Limit Theorem

has a pvalue of 0.0351

1 – 0.0351 = 0.9649

96.49% probability that the mean rent is more than $1100