110 Guilt in decision making. In a Journal of Behavioral Decision Making (Jan., 2007) study of how guilty feelings impact decisions, 57 students were assigned to a guilty state through a reading/writing task. Immediately after the task, the students were presented with a decision problem where the stated option has predominantly negative features

(e.g., spending money on repairing a very old car). Of these 57 students, 45 chose the stated option. Suppose 10 of the 57 guilty-state students are selected at random. Define x as the number in the sample of 10 who chose the stated option.

a. Find P(x = 5) .

b. Find P(x = 8) .

c. What is the expected value (mean) of x ?