Announcements Modules Extra Credit 2. You and another student are playing a number guessing game against the instructor. A random integer will be chosen from 1 to 399. You and the other student each get a guess at the number and the instructor, who only gets 1 pick, will go last. Whoever gets closest to the random number when it is chosen is the winner. You and the other student are considered a team, trying to beat the instructor. a) If you were the first student to pick, what integer should you choose to give your team the best chance of winning the game? Assume the second student and the instructor are good at the game. b) If you were the second student, and the first student chose the number 345 , then what integer should you choose to give your team the best chance of winning the game?

Step 1 ：In a number guessing game, a random integer is chosen from 1 to 399. Two students and an instructor each get a guess at the number. The one who gets closest to the random number is the winner. The two students are considered a team, trying to beat the instructor.

Step 2 ：For part a), the first student should choose a number that divides the range into two equal parts to cover the maximum possible range of numbers. Therefore, the middle number of the range from 1 to 399 should be chosen. The calculation is \((1+399)/2 = 200\).

Step 3 ：For part b), if the first student chose the number 345, then the second student should choose a number that divides the remaining range into two equal parts. The remaining range is from 1 to 344 and from 346 to 399. The middle number of the larger range should be chosen to cover the maximum possible range of numbers. The calculation is \((1+344)/2 = 172.5\). Since only an integer can be chosen, either 172 or 173 should be chosen.

Step 4 ：Final Answer: For part a), the first student should choose the integer \(\boxed{200}\) to give the team the best chance of winning the game. For part b), the second student should choose the integer \(\boxed{172}\) to give the team the best chance of winning the game.