Question

A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive's employer has offered to buy the house for $207,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $228,000.

(a)

If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price? Let x = sales price.

f(x) =

,              $200,000 ≤ x ≤ $228,000

,              elsewhere

(b)

If she leaves it on the market for another month, what is the probability she will get at least $221,000 for the house?

(c)

If she leaves it on the market for another month, what is the probability she will get less than $207,000?

(d)

Should the executive leave the house on the market for another month? Why or why not?

If the executive leaves the house on the market for another month, the expected sales price in dollars will be $ . This is a

price than if the house is sold back to the company for $207,000. However, if the house is left on the market for another month, there is a probability that the executive will get less than the company offer of $207,000. It is a close call. But the expected value suggests the executive leave the house

Answer 1

a)

f(x) = 1/28000 for $200,000 ≤ x ≤ $228,000

b)

probability she will get at least $221,000 for the house =P(X>221000)=(228000-221000)/28000=7000/28000=0.25

c)

probability she will get less than $207,000 =(207000-200000)/28000 =0.25

d)

f the executive leaves the house on the market for another month, the expected sales price in dollars will be 214000. This is a

higher price than if the house is sold back to the company for $207,000. However, if the house is left on the market for another month, there is a probability that the executive will get less than the company offer of $207,000. It is a close call. But the expected value suggests the executive leave the house