18. Correct. The answer is false.

10%, 25%, and 75% are percentiles of the income distribution. First, we have to obtain the distribution function from the density in problem 16:

The 10%-ile is the value of 'a' for which P (X ≤ a) = 10%. The solution is (18a²-a⁴)/81 = 0.1. Using the solution method of problem 16, we have that a ≈ 0.68 (US$ 680).

The 25%-ile is the value of 'a' such that (18a²-a⁴)/81 = 0.25, and you can find a ≈ 1.098 (US$ 1098).

The 75%-ile is the value of 'a' such that (18a²-a⁴)/81 = 0.75, and you can find a ≈ 2.121 (US$ 2121).