Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,400 houses. The subdivision was built in 1983. A sample of 110 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $227,000, with a standard deviation of $8,500, what is the probability that the sample average is greater than $228,500?

3.22% probability that the sample average is greater than $228,500

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 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 Theorem

The 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 sample average is greater than $228,500?

This is 1 subtracted by the pvalue of Z when X = 228500. So

By the Central Limit Theorem

has a pvalue of 0.9678

1 - 0.9678 = 0.0322

3.22% probability that the sample average is greater than $228,500

360 different combinations

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude