39. Selling a House.

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.

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

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

e. What is the probability the executive will receive exactly $220,000 for the house?

f. Find the probability that the executive gets an offer between $220,000 and 230,000 fo the house.

Amazon Alexa App Downloads. Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In 2018, the Amazon Alexa app was downloaded some 2800 times per day from the Google Play store (AppBrain website). Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2800 and standard deviation of 860.

a. What is the probability there are 2000 or fewer downloads of Amazon Alexa in a day?

b. What is the probability there are between 1500 and 2500 downloads of Amazon Alexa in a day?

c. What is the probability there are more than 3000 downloads of Amazon Alexa in a day?

d. What is the probability that fewer than 3500 downloads of Amazon Alexa occur in a day?