A group of students are rolling a six-sided number cube. The table shows the resulting probability of each outcome for each student.
Person
1
2
3
4
5
6
Naomi
5%
25%
10%
40%
5%
15%
Leila
17%
11%
15%
18%
12%
18%
Chase
17%
25%
10%
8%
30%
10%
Doug
15%
10%
15%
10%
40%
10%
Which student’s experimental probability is the MOST consistent with the theoretical probability of rolling a six-sided number cube?
A
Naomi
B
Leila
C
Chase
D
Doug
The probability of any number is 1/6 = about .18. Which person is closest to that?
1/6 = 0.166666 or about 16% for each possible outcome
How much does each differ from 16% ?
square differences from 16 and add and compare.
Just looking I bet it is Leila.
Which student’s experimental probability is the MOST consistent with the theoretical probability of rolling a six-sided number cube?
To determine which student's experimental probability is the most consistent with the theoretical probability of rolling a six-sided number cube, we need to compare their experimental probabilities to the theoretical probabilities.
The theoretical probability of rolling any specific number on a fair six-sided number cube is 1/6 or approximately 16.67%.
Let's calculate the differences between the theoretical probabilities and each student's experimental probabilities:
- Naomi's difference: 5% - 16.67% = -11.67%
- Leila's difference: 17% - 16.67% = 0.33%
- Chase's difference: 17% - 16.67% = 0.33%
- Doug's difference: 15% - 16.67% = -1.67%
From the differences calculated, we can see that Leila and Chase's experimental probabilities are the closest match to the theoretical probability of 16.67%. Both have a difference of only 0.33%. However, they differ in individual probabilities.
Comparing their individual probabilities, we can see that Leila has a more consistent distribution across the outcomes. Her percentages vary by a smaller range compared to Chase's percentages.
Therefore, the student whose experimental probability is the most consistent with the theoretical probability of rolling a six-sided number cube is:
B) Leila.