Problem -
Every home football game for the past 8 years at Southwestern University has been sold out. The revenues from ticket sales are significant, but the sale of food, beverages, and souvenirs has contributed greatly to the overall profitability of the football program. One particular souvenir is the football program for each game. The number of programs sold at each game is described by the probability distribution given in the following table.
|
Number of Programs Sold
|
Probability
|
|
2,300
|
0.15
|
|
2,400
|
0.22
|
|
2,500
|
0.24
|
|
2,600
|
0.21
|
|
2,700
|
0.18
|
Each program costs $.80 to produce and sells for $2.00. Any programs that are not sold are donated to a recycling center and do not produce any revenue.
a) Simulate the sales of programs at 10 football games. Use the last column in the random-number table (Table F.4) and begin at the top of the column.
b) If the university decided to print 2,500 programs for each game, what would the average profits be for the 10 games that were simulated?
c) If the university decided to print 2,600 programs for each game, what would the average profits be for the 10 games that were simulated?
Table F.4 - Table of 2-Digit Random Numbers
52 06 50 88 53 30 10 47 99 37 66 91 35 32 00 84 57 07
37 63 28 02 74 35 24 03 29 60 74 85 90 73 59 55 17 60
82 57 68 28 05 94 03 11 27 79 90 87 92 41 09 25 36 77
69 02 36 49 71 99 32 10 75 21 95 90 94 38 97 71 72 49
98 94 90 36 06 78 23 67 89 85 29 21 25 73 69 34 85 76
96 52 62 87 49 56 59 23 78 71 72 90 57 01 98 57 31 95
33 69 27 21 11 60 95 89 68 48 17 89 34 09 93 50 44 51
50 33 50 95 13 44 34 62 64 39 55 29 30 64 49 44 30 16
88 32 18 50 62 57 34 56 62 31 15 40 90 34 51 95 26 14
90 30 36 24 69 82 51 74 30 35 36 85 01 55 92 64 09 85
50 48 61 18 85 23 08 54 17 12 80 69 24 84 92 16 49 59
27 88 21 62 69 64 48 31 12 73 02 68 00 16 16 46 13 85
45 14 46 32 13 49 66 62 74 41 86 98 92 98 84 54 33 40
81 02 01 78 82 74 97 37 45 31 94 99 42 49 27 64 89 42
66 83 14 74 27 76 03 33 11 97 59 81 72 00 64 61 13 52
74 05 81 82 93 09 96 33 52 78 13 06 28 30 94 23 37 39
30 34 87 01 74 11 46 82 59 94 25 34 32 23 17 01 58 73
59 55 72 33 62 13 74 68 22 44 42 09 32 46 71 79 45 89
67 09 80 98 99 25 77 50 03 32 36 63 65 75 94 19 95 88
60 77 46 63 71 69 44 22 03 85 14 48 69 13 30 50 33 24
60 08 19 29 36 72 30 27 50 64 85 72 75 29 87 05 75 01
80 45 86 99 02 34 87 08 86 84 49 76 24 08 01 86 29 11
53 84 49 63 26 65 72 84 85 63 26 02 75 26 92 62 40 67
69 84 12 94 51 36 17 02 15 29 16 52 56 43 26 22 08 62
37 77 13 10 02 18 31 19 32 85 31 94 81 43 31 58 33 51