Question

the following dot - plot gives the sale prices for 40 houses in ames, iowa, sold during a recent month. the mean sale price was $203,388 with a standard deviation of $87,609.
(a) find the percentile of the house represented by the red dot.
(enter an integer.)
(b) calculate and interpret the standardized score (z - score) for the house represented by the red dot, which sold for $234,000.
z = - 0.35. this home has a sale price that is $350 below the mean sale price.
z = - 0.35. this home has a sale price that is 0.35 standard deviations below the mean sale price.
z = 0.35. this home has a sale price that is $350 above the mean sale price.
z = 0.35. this home has a sale price that is 0.35 standard deviations above the mean sale price.

Explanation:

Step1: Use z - table for percentile

We know that if we have a z - score, we can find the percentile from the standard normal distribution table. For a z - score of \(z=- 0.35\), we look up the value in the standard normal table. The value corresponding to \(z =-0.35\) in the standard - normal table is \(0.3632\). To convert this to a percentile, we multiply by 100. So the percentile is approximately \(36\)th percentile.

Step2: Interpret z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. A z - score of \(z=-0.35\) means that the value \(x\) is \(0.35\) standard deviations below the mean \(\mu\).

Answer:

(a) 36
(b) \(z=-0.35\). This home has a sale price that is \(0.35\) standard deviations below the mean sale price.