The Uniform Distribution · Exercise 10

The data that follow are the square footage (in 1,000 feet squared) of 28 homes.
$$\begin{array}{ccccccc}\text{1.5}& \text{2.4}& \text{3.6}& \text{2.6}& \text{1.6}& \text{2.4}& \text{2.0}\\ \text{3.5}& \text{2.5}& \text{1.8}& \text{2.4}& \text{2.5}& \text{3.5}& \text{4.0}\\ \text{2.6}& \text{1.6}& \text{2.2}& \text{1.8}& \text{3.8}& \text{2.5}& \text{1.5}\\ \text{2.8}& \text{1.8}& \text{4.5}& \text{1.9}& \text{1.9}& \text{3.1}& \text{1.6}\end{array}$$

The sample mean = 2.50 and the sample standard deviation = 0.8302.

The distribution can be written as X ~ U(1.5, 4.5).

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.

OpenStax, Introductory Statistics 2e · §5.2 The Uniform Distribution · Exercise 10