The uniform distribution of a random variable X is given in the figure below.

Question

From the figure, what is the probability that a randomly selected X is between 0.36 and 1.56? Round your answer to two decimal places.

Answer 1

Hi Bailey,

The area of the uniform distribution is always 1. Recall that the formula for area of any rectangle is:

A=lw, where l=length, w=width

So, here,

A=1

L=2, from length of x-axis

1=2w

w=1/2

Now, the area you were asked to calculate was 0.36 to 1.56. That, for our purposes, is a length, so we subtract:

1.56-0.36=1.2

Now, probability under a uniform curve is an area, so:

L=1.2

w=1/2, held constant

A=(1.2)(1/2)

A=0.60

I hope this helps.