Respuesta :
Answer:
In both Florida and Ohio the house is 2.5 standard deviations from the mean.
Step-by-step explanation:
Z-score
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.
In this problem:
The 200,000 house would be closer to the mean in the state in which the absolute value of the z-score is smaller.
Florida:
[tex]\mu = 240000, \sigma = 16000[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200000 - 240000}{16000}[/tex]
[tex]Z = -2.5[/tex]
In Florida, a home priced at $200,000 is 2.5 standard deviations from the mean.
Ohio:
[tex]\mu = 170000, \sigma = 12000[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200000 - 170000}{12000}[/tex]
[tex]Z = 2.5[/tex]
In Ohio, it is also 2.5 standard deviations from the mean.
In both Florida and Ohio the house is 2.5 standard deviations from the mean.
