Choosing portable grill displays. Refer to the Journal of Consumer Research (March 2003) marketing study of influencing consumer choices by offering undesirable alternatives, Exercise 3.109 (p. 199). Recall that 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-sized grill). The table shows the grill display combinations and the number of times each was selected by the 124 students. Suppose one of the 124 students is selected at random. Let x represent the sum of the grill numbers selected by this student. (This value 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? Grill Display Combination Number of Students 1-2-3 35 1-2-4 8 1-2-5 42 2-3-4 4 2-3-5 1 2-4-5 34 Source: Based on R. W. Hamilton, “Why Do People Suggest What They Do Not Want? Using Context Effects to Influence Others’ Choices,” Journal of Consumer Research, Vol. 29, March 2003 (Table 1). GRILL