Question

in a recent national survey the mean price for a 2000 square-foot home in Florida is $240,000 with a standard deviation of $16,000. The mean price for the same sized home in Ohio is 17,000 with a stand deviation of $12,000.

In which city would a home oriced at $200,000 be vloser to the mean price, compared to the distribution of prices in the city?

Find the z-score corresponding to each city.

Answer 1

Note : I think by mistake the mean price in Ohio was entered as 17000 instead of 170000, because 17000 is far away from 200000.

I have taken both 17000 as the mean price in 1st case and 170000 in 2nd case

Case1 is what is given in the question where mean price in Ohio is 17000

Case 1:

Given the mean price for a 2000 square-foot home in Florida is $240,000 with a standard deviation of $16,000

So _f = 240000

_f = 16000

z-score = (X - _f) / _f

Here given X = 200000

z-score = (200000 - 240000) / 16000

= -40000 / 16000

= -2.5

Given the mean price for a 2000 square-foot home in Ohio is $17,000 with a standard deviation of $12,000

So _O = 17000

_O = 12000

z-score = (X - _O) / _O

Here given X = 200000

z-score = (200000 - 17000) / 12000

= 183000 / 12000

= 15.25

The z-score tells us how far above or below the mean price, the given price is

If the z-score is negative, it implies that the price is less than the mean price

If the z-score is positive, it implies that the price is more than the mean price

Here z-score for florida is -2.5 which is closer to 0, than the z-score for Ohio which is 15.25

So in Florida city, the price is closer to the mean price

Case 2:

Given the mean price for a 2000 square-foot home in Florida is $240,000 with a standard deviation of $16,000

So _f = 240000

_f = 16000

z-score = (X - _f) / _f

Here given X = 200000

z-score = (200000 - 240000) / 16000

= -40000 / 16000

= -2.5

Given the mean price for a 2000 square-foot home in Ohio is $170,000 with a standard deviation of $12,000

So _O = 170000

_O = 12000

z-score = (X - _O) / _O

Here given X = 200000

z-score = (200000 - 170000) / 12000

= 30000 / 12000

= 2.5

The z-score tells us how far above or below the mean price, the given price is

If the z-score is negative, it implies that the price is less than the mean price

If the z-score is positive, it implies that the price is more than the mean price

Here z-score for florida is -2.5 and z-score for Ohio is +2.5 which are at same distance from 0

So in both citities, the price is equally closer to the mean score