Question

yolanda and her family are relocating to los angeles and have found a great area in which to live. the mean price among the homes in the area is $725,000 with a standard deviation of $13,050. they purchased a home for $705,000. (a) find the z-score of the price of yolandas home relative to the prices among the homes in the area. round your answer to two decimal places. z = (b) fill in the blanks to interpret the z-score of the price of yolandas home. make sure to express your answer in terms of a positive number of standard deviations. yolandas home price was standard deviations select above or below the mean price among the homes in the area.

Explanation:

Part (a)

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the mean of the dataset, and $\sigma$ is the standard deviation of the dataset.
Here, $x = 705000$, $\mu=725000$, and $\sigma = 13050$.

Step2: Substitute values into the formula

Substitute the given values into the z - score formula:
$z=\frac{705000 - 725000}{13050}$
First, calculate the numerator: $705000-725000=- 20000$
Then, divide by the standard deviation: $z=\frac{-20000}{13050}\approx - 1.53$ (rounded to two decimal places)

The absolute value of the z - score we found in part (a) is approximately $1.53$. Since the z - score is negative, it means that the value (Yolanda's home price) is below the mean. So we say Yolanda's home price was $1.53$ standard deviations below the mean price among the homes in the area.

Answer:

$-1.53$

Part (b)