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 $210,000, 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 $225,000.

If she leaves the house on the market for another month, what is the probability density function for the sales price? Note: x is in thousands of dollars.

If she leaves it on the market for another month, what is the probability she will get at least $215,000 for the house?

If she leaves it on the market for another month, what is the probability she will get less than $210,000?

What is the expected selling price of the house if the executive waits one month (in dollars)?

Given that 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 $225,000

Let X be the price of the house by leaving in another month in thousands

X is Uniform

Ranges are 200 and 225

Hence pdf of X is

a) [tex]f(x) = \frac{1}{25}= , 200<X<225[/tex]

b) [tex]P(X\geq 215) = \frac{215-200}{25} \\=0.60[/tex]

c) [tex]P(X<210.000) = \frac{210-200}{25} =0.40[/tex]

d) Expected selling price = E(X) = [tex]\frac{200+225}{2} =212.5[/tex]

~212500 dollars in actual