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

Answer: 34.56