Partway through the fall, the football team at a Big 12 university has nine games remaining in its season. The probability of winning each game is 0.7. The outcomes of games are independent. Let X be the number of the remaining nine games that the team wins.

NOT CONTINUED. If the team wins at least seven of the remaining nine games, the team will be in a bowl game. Being in a bowl game brings in an additional $1,000,000 in revenue. The university wants to offer the coach a one-time bonus now to get him to sign a new contract. What is the largest bonus they can give the coach that leaves the university with an expected $200,000 in bowl game revenue, after the bonus is paid? Integer