freedom.) 12.15. Two dice are thrown together 360 times, and the total score is re- corded for each throw. The possible totals are 2, 3, . . . , 12, and their numbers of occurrences are as shown in Table 12.15. (a) Calculate the probabilities for each Table 12.15. Observed occurrences of total scores for two dice thrown together 360 times; for Problem 12.15. 2 3 4 5 7 Total score: 6 8 10 11 12 6 14 Occurrences: 35 57 50 44 49 39 27 16 total and hence the expected number of occurrences (assuming the dice are true). (b) Calculate x, d, and =xld. (c) Assuming the dice are true, what is the probability of getting a value of this large or larger? (d) At the 5% level of significance, can you reject the hypothesis that the dice are true? At the 1% level? 23

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Chapter1: Combinatorial Analysis
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freedom.)
12.15. Two dice are thrown together 360 times, and the total score is re-
corded for each throw. The possible totals are 2, 3, . . . , 12, and their numbers of
occurrences are as shown in Table 12.15. (a) Calculate the probabilities for each
Table 12.15. Observed occurrences of total scores for two dice thrown together 360
times; for Problem 12.15.
2
3
4
5
7
Total score:
6
8
10
11
12
6
14
Occurrences:
35
57
50
44
49
39
27
16
total and hence the expected number of occurrences (assuming the dice are true).
(b) Calculate x, d, and =xld. (c) Assuming the dice are true, what is the
probability of getting a value of this large or larger? (d) At the 5% level of
significance, can you reject the hypothesis that the dice are true? At the 1% level?
23
Transcribed Image Text:freedom.) 12.15. Two dice are thrown together 360 times, and the total score is re- corded for each throw. The possible totals are 2, 3, . . . , 12, and their numbers of occurrences are as shown in Table 12.15. (a) Calculate the probabilities for each Table 12.15. Observed occurrences of total scores for two dice thrown together 360 times; for Problem 12.15. 2 3 4 5 7 Total score: 6 8 10 11 12 6 14 Occurrences: 35 57 50 44 49 39 27 16 total and hence the expected number of occurrences (assuming the dice are true). (b) Calculate x, d, and =xld. (c) Assuming the dice are true, what is the probability of getting a value of this large or larger? (d) At the 5% level of significance, can you reject the hypothesis that the dice are true? At the 1% level? 23
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