QUESTION 1 [Include all of your answers in a SINGLE document and attach that doc

Question

QUESTION 1 [Include all of your answers in a SINGLE document and attach that document at the end of the exam. Label each answer clearly. Please begin each problem on a new page/sheet. Point values are indicated in the question body below.] Problem 1: All 50 students in a Managerial Decision Making class were polled about their opinion of the Boston Red Sox The responses to the statement "The Red Sox will win the 2016 World Series" were as follows: Numeric Number of Value Response Agree Neutral Disagree Responses 25 20 2 0 For each item below, please show your work and/or explain your reasoning to receive full credit a). Find a probability distribution for these results; that is, compute the probability of each response. [6 pts] b). Let Xbe the numeric value of the response. What is the expected value of X? [4 pts c). Compute the variance of the random variable X. [6 pts]

Explanation / Answer

a. total number of responses=20+25+5 = 50

probability of Agree = 25/50

probability of Neutral = 20/50

probability of Disagree = 5/50

b. E [X] = sum of (probability * numeric values)

E[X] = 1.4

c. V[X] =E[X2] - E[X]2

E[X2] = 2.4

V[X] = 2.4 - (1.4)2 = 0.44

Numeric value number of responces probability 2 25 0.5 1 20 0.4 0 5 0.1 Total 50

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