Your client is going to be travelling to Las Vegas in the near future and he wants to place some bets on his favorite professional baseball team.To ensure he knows the odds on his bets he wants to know the probability of certain scenarios occurring.

1. Knowing that the team has won an average of 95 games over the past three seasons and that there are 162 games in a season, estimate the probability of the team winning any single game in the upcoming season.

2. Using the information from number 1, determine the probability that the team will win exactly 100 games in the upcoming season.

3. Using the information from number 1, determine the probability of the team winning at least 100 games in the upcoming season.

4. Using the information from number 1, determine the probability of the team winning less than 100 games.

5. Working in parallel with you, a coworker found the probability of the team winning less than 100 games to be 80.96%. Do these results match yours? If not, identify the error that was made.

6. What assumptions must be made in this scenario that allow us to use a binomial distribution?What are some possible reasons why a binomial distribution may not accurately represent the scenario?