Question

1) The graph shows a probability distribution.

Answer 1

1. $P(X$ is the area under the curve to the left of $x=5$, which is a trapezoid with "bases" of length 2 and 5 and "height" 0.2, so

$P(X$

2. Find the area under the curve for each of the specified intervals:

$P(X\le2)=\dfrac{2\cdot0.2}2=0.2$ (triangle with base 2 and height 0.2)

$P(X\ge4)=\dfrac{1\cdot0.4}2=0.2$ (triangle with base 1 and height 0.4)

$P(2\le X\le4)=\dfrac{0.2+0.4}2\cdot2=0.6$ (trapezoid with "bases" 0.2 and 0.4 and "height" 2)

$P(1\le X\le3)=\dfrac{0.1+0.3}2\cdot2=0.4$ (trapezoid with "bases" 0.1 and 0.3 and "height" 2)