Question

What is P(4 ≤ X ≤ 6)? Explain.
If P(X ≤ a) = 0.2, what is a? Explain.

Answer 1

(a) 0.4

(b) a = 3

Explanation:

(a) The area under the curve from x=4 to x=6 is 0.2 units high and 2 units wide, so is 0.2·2 = 0.4. (The area of a rectangle is the product of length and width.)

(b) The area is 0.2 and the height of the curve is 0.2, so the width of the region of concern is 0.2/0.2 = 1. (Again, area = height·width, or width = area/height.) 1 unit from the left end is found at X=3, so a = 3.