Statistical Analysis for Business Spring 2017 CASE Assignment 1 Overview The obj

Question

Statistical Analysis for Business Spring 2017 CASE Assignment 1 Overview The objective of this case is to introduce you to statistics and reinforce your concepts of expected value and binomial distributions Assignment: Your case deals primarily with the concepts of expected value and binomial distributions. This case will be based upon the 2017 NCAA NIT basketball tournament that will begin next week. There will be a lot of news coverage and people talking about brackets and who is going to win the whole tournament, or how they did with their picks. The president of the United States even releases his picks in probably more coverage then when the budget is rolled out. And we have been fortunate to have our own school participate in the tournament in the past couple of years. In previous years Quicken Loans and Warren Buffet offered to give a billion dollars to anyone who got a perfect bracket (picked every team correctly) On one sheet of paper, I would like you to calculate the total number of points you could receive if you got every selection right, the maximum points that are available during each round, the expected number of points that a person would get for the whole tournament, and how many different brackets you would have to pick in order to guarantee yourself getting all the points (four questions) Please show work where practical and to support your answers. Clearly label each question or answer. You can answer the questions in an executive summary format or list them in order. Please describe how you came to the answer in words and use calculations to support your answer. The descriptions can be simple and composed in one or two sentences

Explanation / Answer

Part 1. Total number of points I recieve if I got every selection right

Total = Sum of ( total games at each round * points per game ) = 16*2 + 8*3 + 4*8 + 2* 20 + 1*50

= 32 + 24 + 32 + 40 + 50 = 178 points

Total number of points I recieve if I got every selection right = 178

Part 2. Maximum points that are available each round = No of games in each round * points per game

First Round = 16*2 = 32 points

Sweet 16 = 8 * 3 = 24 points

Elite 8 = 4 * 8 = 32 points

Final 4 = 2 * 20 = 40 points

Championship Game = 1 * 50 = 50 points

Part 3. The expected number of points a person would get for the whole tournament (E(X))

probability of getting a team correct = 1/ 2 = 0.5

E(X) = sum of (no of games * probability * points)

= 16*0.5*2 + 8*0.5*3 + 4*0.5*8 + 2*0.5*20+ 1*0.5*50 = 0.5 * Total points = 0.5 * 178 = 89

Part 4. No Of brackets to pick to guarantee I get all the points

At each round we need two brackets to guarantee getting all points for that round.

Hence total no of brackets = (no of brakets for round 1 )*(No of brackets for round 2) *....(No of brackets in round 5)

= 2*2*2*2*2 = 25 = 32 brackets

No Of brackets to pick to guarantee I get all the points = 32 brackets.

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