Chapter 2.1, Problem 28E

(a)

To determine

To explain:the reason for satisfying the requirements for a density curve

Answer to Problem 28E

As the curve is on or above the horizontal axis everywhere, and it forms a density of 1 by 1 rectangle; therefore, the area beneath the curve is 1.

Explanation of Solution

Given:

  

As the curve is on or above the horizontal axis everywhere, and it forms a density of 1 by 1 rectangle; therefore, the area beneath the curve is 1.

  

Conclusion:

Therefore the given curve satisfies the two requirements of density curve.

(b)

To determine

To find: the percent of the observations that are greater than 0.8

Answer to Problem 28E

20% of the observations lie above 0.8.

Explanation of Solution

Given:

  

Calculation:

The area under the uniform distribution between 0.8 and 1 is (1-0.8) × 1 = 0.2. So 20% of the observations lie above 0.8.

  

Conclusion:

So 20% of the observations lie above 0.8.

(c)

To determine

To find: percent of the observations lie between 0.25 and 0.75

Answer to Problem 28E

50% of the observations lie between 0.25 and 0.75.

Explanation of Solution

Given:

  

Calculation:

The area under the uniform distribution between 0.25 and 0.75 is (0.75 -0.25) × 1=0.5.

So 50% of the observations lie between 0.25 and 0.75.

  

Conclusion:

So, 50% of the observations lie between 0.25 and 0.75.