Suppose you randomly choose an integer n between 1 to 5, and then draw a circle with a radius of n centimetres. what is the expected area of this circle to the nearest hundredths of a square centimetres?

The set of possible integers is 1, 2, 3, 4, and 5.

The area of a circle with radius of n centimeters = π(n)^2.

So, the set of possible values are:

n       area = π(n^2)

1       π

2       4π

3       9π

4       16π

5       25π

And the expected value of the area may be determined as the mean (average) of the five possible areas:

expected value of the area = [ π+ 4π + 9π + 16π + 25π] / 5 = 11π ≈ 34.5575, which rounded to the nearest hundreth is 34.56

34.56