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 206,000, 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 230,000. (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. (b) If she leaves it on the market for another month, what is the probability she will get at least $224,000 for the house? (c) If she leaves it on the market for another month, what is the probability she will get less than $206,000? (d) Should the executive leave the house on the market for another month? Why or why not?
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 206,000, 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 230,000. (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. (b) If she leaves it on the market for another month, what is the probability she will get at least $224,000 for the house? (c) If she leaves it on the market for another month, what is the probability she will get less than $206,000? (d) Should the executive leave the house on the market for another month? Why or why not?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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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 206,000, 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 230,000.
(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.
(b)
If she leaves it on the market for another month, what is the probability she will get at least $224,000 for the house?
(c)
If she leaves it on the market for another month, what is the probability she will get less than $206,000?
(d)
Should the executive leave the house on the market for another month? Why or why not?
(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.
The uniform probability density function for the random variable x is given below.
f(x) =
|
a ≤ x ≤ b | |||
| 0 | elsewhere |
Here, the random variable x is the sales price of a house and is given to be uniformly distributed between 200,000 and 230,000. Therefore, we have a = and b = .
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