Answer:
A a house in that market that sells for $300,000 is unusual.
Step-by-step explanation:
Let the random variable <em>X</em> denote the price of a house and the random variable <em>Y</em> denote the living area of a house.
The number of houses surveyed by the real estate agent is, <em>n</em> = 1057.
Assume that both the random variables, <em>X </em>and <em>Y</em> are approximately normally distributed.
That is,
To compute the probability of a Normal distribution we first need to convert the raw scores to <em>z</em>-scores.
A <em>z</em>-score higher than 1.96 and lower than -1.96 are considered unusual. The values having these <em>z</em>-scores are considered as outliers.
(1)
Compute the <em>z</em>-score for <em>X</em> = 300000 as follows:
(2)
Compute the <em>z</em>-score for <em>Y</em> = 3000 as follows:
The <em>z</em>-score for a house in that market that sells for $300,000 is more than 1.96.
This implies, that the price $300,000 is unusually high.
The complete statement is:
The house that sells for $300 comma 000 has a z-score of <u>2.70</u> and the house with 3000 sq ft has a z-score of <u>1.19</u>.