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Chapter 2: Q 28. (page 108)

A uniform distribution The figure below displays the density curve of a uniform distribution. The curve takes the constant value 1 over the interval from 0

to 1 and is 0 outside the range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1

(a) Explain why this curve satisfies the two requirements for a density curve.

(b) What percent of the observations are greater than 0.8?

(c) What percent of the observations lie between0.25 and 0.75?

Short Answer

Expert verified

Part (a) Because the curve is always on or above the horizontal axis, it forms a 1 by 1 rectangular density; thus, the area beneath the curve is 1

Part (b) 20% of the observations lie above 0.8

Part (c) 50% of the observations lie between 0.25 and 0.75

Step by step solution

01

Part (a) Step 1. Given

02

Part (a) Step 2. Concept

These inflection points are always one standard deviation distant from the mean on a normal density curve.

03

Part (a) Step 3. Explanation

Because the curve is always on or above the horizontal axis, it forms a 1by 1 rectangular density; thus, the area beneath the curve is 1

As a result, the supplied curve meets both of the density curve's conditions.

04

Part (b) Step 1. Explanation

Between 0.8 and 1, the area under the uniform distribution is (1-0.8)脳1=0.2. As a result, 20% of the observations had a value greater than 0.8

As a result, 20% of the observations had a value greater than 0.8

05

Part (c) Step 1. Explanation

Between 0.25 and 0.75, the area under the uniform distribution is (0.75-0.25)脳1=0.5.

As a result, half of the observations are in the 0.25 to 0.75 range.

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