Binomial Distribution Analysis

You have just been hired by G&B Consulting and given your first assignment. A local independently wealthy citizen who likes gambling and baseball, but not math, has asked you to help him determine the likelihood of some different outcomes for the upcoming season.
Background information: Over the past 3 seasons since the current manager took over the team, the team has won an average 92.33 games. There are 162 games in a season.
He will be travelling to Las Vegas shortly and is looking forward to placing some bets and wants to know the following:

What is the best prediction we have for the probability of winning any single game?
What is the probability of the team winning exactly 100 games?
What is the probability of the team winning at least 100 games?
What is the probability of the team winning less than 100 games?

Working in parallel, your coworker came up with the following results:
The probability of the team winning less than 100 games is 90.31%. Do you agree with these results? If not, identify the error made and explain how to correct it.
Create a report using Microsoft Word that you will send to the client. Include in your report the solutions to all questions posed by the client and show all of your work including any formulas used, if you used Excel for any calculations include that in the drop box along with your report. Explain each solution in the context of the scenario. Also include any assumption(s) needed to be made in order to use a binomial distribution and some possible reasons why this assumption may not be valid?
In the same document, compose an email to your coworker about whether or not you agree or disagree with those results and any explanations that may be needed on how to correct an error.

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