# Z-Score Problem

A five-year old study claims that selling prices of new homes / condominiums in the New York area have a normal distribution with mean = $180,000 and standard deviation = $40,000.

a. Assuming that the results of the study are still valid, what is the probability that a randomly selected new house in the New York area will cost more than $210,000?

b. A new couple decides to settle in this area. They are willing to pay between $160,000 and $190,000 for a new home. What is the probability that they will find a new house to purchase in the New York area that satisfies their price range?

c. What is price below which the 10% of the lowest priced new homes in the New York area are sold?

#### Solution Preview

Statistics help - probability

A five-year old study claims that selling prices of new homes / condominiums in the New York area have a normal distribution with mean μ = $180,000 and standard deviation σ = $40,000.

To solve all parts of this problem, we need to use z-scores. The formula for converting a raw score into z-scores is:

z = (x - μ)/σ

where x is the raw value, μ is the population mean, and σ is the population standard deviation.

a. Assuming that the results of the study are still valid, what is the probability that a randomly selected new house in the New York area will cost more than $210,000?

First, let's convert x = 210,000 into a z-score:

z = (210,000 - 180,000)/(40,000) = 30,000/40,000 = ¾ = 0.75

Now we have to convert the z-score into a probability. Z-scores have a normal distribution with a mean of 0 and a standard deviation of 1. The distribution looks like this:

We want to find the probability that a randomly selected house will cost more than $210,000. This is equivalent to ...