Solution Found!
Choosing portable grill displays. Refer to the Journal of
Chapter 4, Problem 24E(choose chapter or problem)
Problem 24E
Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, Exercise 3.23 (p. 142). 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 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).
3.23 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 homes. 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 differentsized grills) were available, but only three displays would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller-sized grill).
a. In how many possible ways can the three grill displays be selected from the five displays? List the possibilities.
b. The table shows the grill display combinations and the number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.
c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.
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 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, No. 4. Mar. 2003 (Table 1).
Questions & Answers
QUESTION:
Problem 24E
Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, Exercise 3.23 (p. 142). 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 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).
3.23 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 homes. 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 differentsized grills) were available, but only three displays would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller-sized grill).
a. In how many possible ways can the three grill displays be selected from the five displays? List the possibilities.
b. The table shows the grill display combinations and the number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.
c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.
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 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, No. 4. Mar. 2003 (Table 1).
ANSWER:
Answer
Step 1 of 2
(a)
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 |
The probability distribution for is given in the table below :
Grill Display Combination |
(sum of the grill numbers selected by this student) |
|
1-2-3 |
6 |
|
1-2-4 |
7 |
|
1-2-5 |
8 |
|
2-3-4 |
9 |
|
2-3-5 |
10 |
|
2-4-5 |
11 |