All 40 students in an Operations Analysis class were polled about their opinion of the Boston Red Sox. The responses to the statement ?The Red Sox will win the 2015 World Series? were as follows:

Response Numeric Value Number of Responses Strongly Agree 5 15 Agree 4 10 Neutral 3 5 Disagree 2 5 Strongly DIsagree 1 5

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.

b). Let X be the numeric value of the response. What is the expected value of X?

c). Compute the variance and standard deviation of the random variable X.

students in an Operations Analysis class were polled about their opinion of the Boston Red Sox. The responses to the statement ½The Red Sox will win the 2015 World Series½ were as follows: Response Numeric Value Number of Responses Strongly Agree 5 15 Agree 4 10 Neutral 3 5 Disagree 2 5 Strongly DIsagree 1 5 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. b). Let X be the numeric value of the response. What is the expected value of X? c). Compute the variance and standard deviation of the random variable X