Question

A professor, transferred from Toronto to New York, needs to sell his house in Toronto quickly. Someone has offered to buy his house for $220,000, but the offer expires at the end of the week. The professor does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with his realtor, the professor believes the price he will get by leaving the house on the market for another month is uniformly distributed between $210,000 and $235,000.
(a) If he leaves the house on the market for another month, what is the probability that he will get at least $225,000 for the house?
(b) If he leaves it on the market for another month, what is the probability he will get less than $217,000?
(c) What is the expected value and standard deviation of the house price if it is left in the market?

Answer 1

Answer:

(a) = 40%

(b) = 28%

(c) Expected value = $222,500

Standard deviation = $7,216.88

Step-by-step explanation:

This is a normal distribution with a = 210,000 and b =235,000

(a) The probability that he will get at least $225,000 for the house is:

$P(X\geq 225,000) =1 -\frac{225,000-a}{b-a} =1-\frac{225,000-210,000}{235,000-210,000} \\P(X\geq 225,000) =0.4= 40\%$

(b)The probability he will get less than $217,000 is:

$P(X\leq 217,000) =\frac{217,000-a}{b-a} =\frac{217,000-210,000}{235,000-210,000} \\P(X\leq 217,000) =0.28= 28\%$

(c) The expected value (E) and the standard deviation (S) are:

$E=\frac{a+b}{2}=\frac{210,000+235,000}{2}\\ E=\ 222,500\\S=\frac{b-a}{\sqrt{12}}=\frac{235,000-210,000}{\sqrt{12}}\\S=\ 7,216.88$