Question

For a continuous probability distribution, 0 ≤ x ≤ 10. What is P(x = 7)?

Answer 1

f(x) = \(\frac{1}{20}\) for 0 ≤ x ≤ 20. x = a real number. The graph of

f(x) = \(\frac{1}{20}\) is a horizontal line. However, since 0 ≤ x ≤ 20, f(x) is restricted to the portion between x = 0 and x = 20, inclusive.

This shows the graph of the function f(x) = 1/20. A horiztonal line ranges from the point (0, 1/20) to the point (20, 1/20). A vertical line extends from the x-axis to the end of the line at point (20, 1/20) creating a rectangle.

f(x) = \(\frac{1}{20}\)for 0 ≤ x ≤ 20.

The graph of f(x) = \(\frac{1}{20}\) is a horizontal line segment when 0 ≤ x ≤ 20.

The area between f(x) = \(\frac{1}{20}\) where 0 ≤ x ≤ 20 and the x-axis is the area of a rectangle with base = 20 and height = \(\frac{1}{20}\).

\(\text{AREA}=20\left(\frac{1}{20}\right)=1\)