Question

based on the density graph below, what is the probability of a value in the sample space being anywhere from 5 to 15?

choice

a. 40%
b. 20%
c. 80%
d. 60%

Explanation:

Step1: Identify the shape and formula

The density graph is a rectangle (uniform distribution). The probability for a uniform distribution is the area of the rectangle, which is \( \text{height} \times \text{width} \).

Step2: Determine the height and width

• The height (density) is \( 0.04 \) (from the graph, the y - axis value for the rectangle).
• The width of the interval from 5 to 15 is \( 15 - 5=10 \).

Step3: Calculate the area (probability)

The area (probability) is \( \text{height} \times \text{width}=0.04\times10 = 0.4 \), which is \( 40\% \).

Answer:

A. 40%