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?
For Information: Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, Exercise 3.23.
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