Question

a) What is the height of the function, f(x)? Give your answer as a reduced fraction.b) What is the probability of the shaded region? Give your answer as a reduced fraction.

Answer 1

Answers:

a) 1/12

b) 1/4

Step-by-step explanation:

In a uniform function that goes from a to b, the height of the function f(x) is equal to:

`f(x)=(1)/(b-a)`

Since the function in the graph goes from 0 to 12, the height of the function f(x) is:

`f(x)=(1)/(12-0)=(1)/(12)`

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:

`P=\text{Base}* Height=(3*(1)/(12))=(3)/(12)=(1)/(4)`

Therefore, the height of the function is 1/12, and the probability of the shaded region 1/4