Solution

Sure, here's a step-by-step solution:

Given that the average of five observations, x, x+2, x+4, x+6, and x+8 is 11.

We can use the formula for the average of a set of numbers:

Average = (sum of the numbers) / (number of the numbers)

Therefore, we have:

11 = (x + (x+2) + (x+4) + (x+6) + (x+8)) / 5

Multiplying both sides by 5, we get:

55 = 5x + 20

Subtracting 20 from both sides, we get:

35 = 5x

Dividing both sides by 5, we get:

x = 7

So, the five observations are 7, 9, 11, 13, and 15.

The last three observations are x+4, x+6, and x+8, which are 11, 13, and 15 respectively, when x is 7. Therefore, the average of the last three observations is:

(11 + 13 + 15) / 3 = 13

Hence, the average of the last three observations is 13.