Answers:
a) 1/12
b) 1/4
Explanation:
In a uniform function that goes from a to b, the height of the function f(x) is equal to:
[tex]f(x)=\frac{1}{b-a}[/tex]
Since the function in the graph goes from 0 to 12, the height of the function f(x) is:
[tex]f(x)=\frac{1}{12-0}=\frac{1}{12}[/tex]
On the other hand, the probability of the shaded region is equal to the area of the shaded region. So, the area is base times height, where the height is 1/12 and the base is 3 units. Then, the probability is:
[tex]P=\text{Base}\times Height=(3\times\frac{1}{12})=\frac{3}{12}=\frac{1}{4}[/tex]
Therefore, the height of the function is 1/12, and the probability of the shaded region 1/4
