Recall the pick a number game where you needed to pick an

Question

Game Theory Question:

1. Recall the "Pick a Number Game," where you needed to pick an integer between 1 and 100, and the winning value is the one that is closest to 3/4 of the average of all the values submitted.

The strategy set for player I  is Si ={1,2,...,100}

Suppose that you believe the following: "None of my classmates will play a dominated strategy and they will choose an undominated strategy at random." (All undominated strategies are equally likely). Which of the following strategy choices is a best response to this belief? 

You can assume that the class size is large enough that the impact of any one person's strategy on the average value is negligible. 

1. 28
2. 42
3. 38
4. 75
5. 1