Choosing portable grill displays. Refer to the Journal of Consumer Research(Mar. 2003) mar...

Choosing portable grill displays. Refer to the Journal of Consumer Research(Mar. 2003) marketing study ofinfluencing consumer choices by offering undesirablealternatives, presented in Exercise. Recallthat each of 124 college students selected showroomdisplays for portable grills. Five different displays (representingfive different–sized grills) were available, but thestudents were instructed to select only three displays inorder 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.

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b. What is the probability that x exceeds 10?

Choosing portable grill displays. University of Maryland marketing professor R. W. Hamilton studied how people attempt to influence the choices of others by offering undesirable alternatives (Journal of Consumer Research, Mar. 2003). Such a phenomenon typically occurs when family members propose a vacation spot, friends recommend a restaurant for dinner, and realtors show the buyer potential homesites. In one phase of the study, the researcher had each of 124 college students select showroom displays for portable grills. Five different displays (representing five different–sized grills) were available, but only three would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller grill).

a. In how many possible ways can the three–grill displays be selected from the 5 displays? List the possibilities.

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b. The next table shows the grill display combinations and number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.

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c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.