Question

Greg is a commercial real estate agent in San Diego. He notes from his records that the length of time that properties spend on the market before being sold appears to be normally distributed. From October 2017 to October 2018, the average time that a property in San Diego spent on the market was approximately 45 days, with a standard deviation of 9 days. Typically, if a property doesn’t sell within 70 days of being listed, Greg’s firm will reduce the asking proce in an attempt to close the sale.

a. what is the probability that a property will be sold within 30 days of being listed?

b. Greg just listed a new property. What is the probability that Greg will end up having to reduce its askin price?

c. While flipping through a local magazine, Greg sees an ad for his own firm in which the marketing department has claimed that ‘most of our properties sell within 40-60 days.’ In reality, what is the probability that a property will sell within that timeframe?

d. A somewhat anxious client has asked Greg to provide an estimate of how long jt will take to close the sale on a newly-listed property. To be safe, Greg decides he should round up his estimates to reduce the chance of being wrong. What is the number of days he should tell the client, such that there is only a 1% chance thag the house won’t actually sell within that time?

Answer 1

Let X denote the no. of days a property spends on the market. Now, we are given that:

a.

The probability that a property will be sold within 30 days of being listed is:

b.

The asking price is reduced if the property doesn't sell in 70 days (X > 70). Thus, the probability that Greg will end up having to reduce the property's asking price is:

c.

The probability of a property selling within 40-60 days is given by:

d.

Here, we need to find a point 'x' such that the probability of X being greater than x is 0.01 (or the probability of X being less than x is 0.99)

From the cdf of standard normal distribution. we know that:

Thus, he should tell the client : 64 days [Answer]

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.