A business executive, transferred from Chicago to Atlanta,...

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 $\$ 225,000$ . 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? b. If she leaves it on the market for another month, what is the probability that she will get at least $\$ 215,000$ for the house? c. If she leaves it on the market for another month, what is the probability that she will get less than $\$ 210,000 ?$ 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 $\$ 210,000,$ 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 $\$ 225,000$ .
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?
b. If she leaves it on the market for another month, what is the probability that she will
get at least $\$ 215,000$ for the house?
c. If she leaves it on the market for another month, what is the probability that she will
get less than $\$ 210,000 ?$
d. Should the executive leave the house on the market for another month? Why or why not?

Key Concepts

Uniform Distribution

This concept refers to a probability distribution in which all outcomes within a certain interval are equally likely. It is characterized by its two parameters, typically representing the minimum and maximum values, and is used to model situations where there is no inherent preference for any number in that range.

Probability Density Function (PDF)

The probability density function is a function that describes the likelihood of a random variable taking on a particular value within a continuous range. In the context of a uniform distribution, the PDF is constant over the interval defined by the minimum and maximum values, and it integrates to 1 over that range.

Cumulative Distribution Function (CDF)

The cumulative distribution function gives the probability that a random variable is less than or equal to a certain value by integrating the probability density function from the lower bound of the distribution up to that value. It is useful for calculating the probability of events within a specified subinterval of the total range.

Decision Analysis Under Uncertainty

This concept involves evaluating different choices by considering the likelihood of various outcomes and their impacts. In scenarios such as selling a house with uncertain market conditions, decision analysis helps in weighing the benefits of accepting a guaranteed offer against the potential gains or losses of waiting, using probabilistic models to inform the decision.

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