Use the theoretical data to calculate the mean, variance, and standard deviation of the theoretical probability distribution. 2) Find the theoretical probability of rolling a sum less than 3. 3) Find the theoretical probability of rolling a sum between (and including) 4 and 7.
|
Sum of dice (X) |
# of ways of obtaining sum |
Relative Frequency of (X) = # of ways of obtaining sum# of possible outcomes |
|---|---|---|
|
2 |
1 way (1+1) |
1/36 |
|
3 |
2 ways (1+2, 2+1) |
2/36 |
|
4 |
3 ways (1+3, 3+1, 2+2) |
3/36 |
|
5 |
4 ways (2+3, 3+2, 4+1, 1+4) |
4/36 |
|
6 |
5 ways (1+5, 5+1, 3+3, 4+2, 2+4) |
5/36 |
|
7 |
6 ways, (6+1, 1+6, 4+3, 3+4, 5+2, 2+5) |
6/36 |
|
8 |
4 ways (3+5, 5+3, 6+2, 2+6) |
4/36 |
|
9 |
4 ways (6+3, 3+6, 5+4, 4+5) |
4/36 |
|
10 |
3 ways (5+5, 6+4, 4+6) |
3/36 |
|
11 |
2 ways (6+5, 5+6) |
2/36 |
|
12 |
1 way (6+6) |
1/36 |
1) Use the theoretical data to calculate the mean, variance, and standard deviation of the theoretical probability distribution.
2) Find the theoretical probability of rolling a sum less than 3.
3) Find the theoretical probability of rolling a sum between (and including) 4 and 7.
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