Question

The Uniform Distribution

Use the following information to answer the next ten questions in excel . The data that follow are the square footage (in 1,000 feet squared) of 28 homes.

1.5	2.4	3.6	2.6	1.6	2.4	2.0
3.5	2.5	1.8	2.4	2.5	3.5	4.0
2.6	1.6	2.2	1.8	3.8	2.5	1.5
2.8	1.8	4.5	1.9	1.9	3.1	1.6

The sample mean = 2.50 and the sample standard deviation = 0.8302. The distribution can be written as X ~ U(1.5, 4.5).

1 What type of distribution is this?

2. In this distribution, outcomes are equally likely. What does this mean?

3 What is the height of f(x) for the continuous probability distribution?

4 What are the constraints for the values of x?

5 What is P(2 < x < 3)?

6. What is P(x < 3.5| x < 4)?

7 What is P(x = 1.5)?

8. What is the 90^th percentile of square footage for homes?

9. Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet.

10 Find the theoretical mean

11 Find the theoretical standard deviation

12 How do these compare to the sample mean and standard deviation?

All must be done in Excel

Answer 1