The average selling price of homes in a certain city is $356,300. Assume the variable is normally distributed with a standard deviation of $64,600. If 396 homes are for sale, how many homes will sell for more than $325,000? (Round up to the next whole number.)

I don't understand how to do this problem. I have a test this weekend and want to understand. It won't be the same question, but one similar. Thanks.

I don't know if you are using some kind of chart for the normal distribution or if you have a "fancy" calculator that can handle that.

The method used by calculators varies from model to model, so I cannot describe it

change your 325000 to a z-score

z-score for 325000 = (325000-356000)/64600
= -.4799
If you have a table, find -.48 (the best you can probably do on the chart) to find .3156
So the prob that the house will cost MORE than 325000 is
1 - .3156 or .6844

so number sold at that range is .6844(396) or 271 homes

To find out how many homes will sell for more than $325,000, we need to calculate the z-score and then use the z-table to find the corresponding probability.

1. Find the z-score:
The z-score measures the number of standard deviations a data point is from the mean. We can find the z-score using the formula:
z = (x - μ) / σ
where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

In this case, x = $325,000, μ = $356,300, and σ = $64,600.

z = (325000 - 356300) / 64600
= -31300 / 64600
≈ -0.485

2. Use the z-table:
The z-table provides the area under the normal distribution curve for different z-scores. We want to find the area to the right of the z-score -0.485, which represents the probability of selling a home for more than $325,000.

However, since we are dealing with a negative z-score, we need to find the area to the left of the z-score (-0.485) and then subtract it from 1 to get the desired result.

Using the z-table, we find that the area to the left of -0.485 is approximately 0.3157.

So, the area to the right of -0.485 is 1 - 0.3157 ≈ 0.6843.

3. Calculate the number of homes:
Now we can multiply the probability of selling a home for more than $325,000 (0.6843) by the total number of homes available (396) to find how many homes will sell for more than $325,000.

Number of homes = Probability x Total number of homes
= 0.6843 x 396
≈ 270.98

Since we need to round up to the next whole number, the estimated number of homes that will sell for more than $325,000 is 271.

It's important to note that this is an estimated calculation based on the assumption of a normal distribution. In real life, actual results may vary.