Probabilities about House Sales: Number of Days to Sell

5. A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.

a. Assuming the company's claim is true, if one home is selected at random, what is the probability that it will be sold in less than 63 days?

b. Assuming the company's claim is true, if a random sample of 9 homes is selected, what is the probability that the mean selling time will be less than 63 days?

c. Assuming the company's claim is true, if a random sample of 64 homes is selected, there is a 75% probability that the sample mean is greater than how many days?

d. Do you have to know that selling times are normally distributed to answer part (c)? Explain why or why not.

e. Suppose you doubt the company's claim that their average selling time is 57 days. To test their claim, you select a random sample of 64 homes and the sample mean number of days to sell those homes is 62 days. Do you have evidence to refute the company's claim? Explain why or why not.

Solution Preview

A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.

a. Assuming the company’s claim is true, if one home is selected at random, what is the probability that it will be sold in less than 63 days?

The solution calculates the probability of the selling times of a random sample of houses and determines if the selling times are normally distributed.

The sales records of a real estate agency show the following sales over the past 200 days:
Number of NumberHouses Sold of Days
0 60
1 80
2 40
3 16
4 4
a. How many sample points are th

#53. A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnel that returns him to his cell after 2 days travel. The second leads to a tunnel that returns him to his cell after 4 days travel. The third door leads to freedom after 1 day of travel. If it is assumed that the prisoner will always select do

A market in Boston orders oranges from Florida. The oranges are shipped to Boston from Florida by either railroad, truck, or airplane; an order can take 1, 2, 3, or 4 days to arrive in Boston once it is placed. The following probabilities have been assigned to the number of days it takes to receive an order it is placed (referre

A major hat store chain is having a sale on three nationally known brands, A, B and C. Probabilities that Brand A, Brand B or Brand C will not be big sellers are: 0.30, 0.40, and 0.50, respectively. All three brands are manufactured by three independent companies.
Calculate the probability that:
a. None of the brands will b

Middleton's has sales for the year of $311,400, cost of goods sold equal to 74 percent of sales, and an average inventory of $42,800. The profit margin is 6 percent and the tax rate is 34 percent. How many days on average does it take the firm to sell an inventory item?

Dividing days by months. For how many days of the year do you get a whole number when you divide the day number by the month number? For example, for December 24, the result of 24 divided by 12 is 2.

1. A mail order company tracks the number of returns it receives each day. Information for the last 50 days shows
Number of returns Number of days
0 - 99 6
100 - 199 20
200 - 299 15
300 or more 9
a. How many sample points are there?
b. List and

Kent can Paint a certain house by himself in x days. His helper Keith can paint the same house by himself in x + 3 days.
Suppose that they work together on the job for 2 days.
To complete the table, use the fact that the work completed is the product of the rate and the time.
Write a Rational expression for the fraction of th

You own a house that you rent for $1,200 a month. The maintenance expenses on the house average $200 a month. The house cost $89,000 when you purchased it several years ago. A recent appraisal on the house valued it at $210,000. The annual property taxes are $5,000. If you sell the house you will incur $20,000 in expenses.You ar