29 Choosing portable grill displays. In a Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, each of 124 college students selected showroom displays for portable grills. Five different displays (representing five different-sized grills) were available, but the students were instructed to select only three displays in order to maximize purchases of Grill #2 (a smaller grill). The table that follows shows the grill display combinations and number of each selected by the 124 students. Suppose 1 of the 124 students is selected at random. Let x represent the sum of the grill numbers selected by that student. (This sum is an indicator of the size of the grills selected.)

a. Find the probability distribution for x .

b. What is the probability that x exceeds 10?

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Grill Display Combination 1-2-3 1-2-4 Number of Students 35 8 1-2-5 2-3-4 2-3-5 2-4-5 42 4 1 34 Based on Hamilton, R. W. "Why do people suggest what they do not want? Using context effects to influence others' choices." Journal of Consumer Research, Vol. 29, Mar. 2003 (Table 1).