The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. The mean price of the same sized home in OH i

Question

The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
Find the z score for each state.

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Calantha 1 month 2021-08-12T07:58:27+00:00 1 Answers 1 views 0

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    2021-08-12T07:59:40+00:00

    Answer:

    The z-score for a home priced at $200,000 in Florida is of -2.5.

    The z-score for a home priced at $200,000 in Ohio is of 2.5.

    The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.

    Step-by-step explanation:

    Z-score:

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

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

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

    The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. Home of $200,000.

    This means that \mu = 240, \sigma = 16, X = 200. So

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

    Z = \frac{200 - 240}{16}

    Z = -2.5

    The z-score for a home priced at $200,000 in Florida is of -2.5.

    The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Home of $200,000.

    This means that \mu = 170, \sigma = 12, X = 200. So

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

    Z = \frac{200 - 170}{12}

    Z = 2.5

    The z-score for a home priced at $200,000 in Ohio is of 2.5.

    Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?

    The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.

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