To determine how the experimental probability compares to the theoretical probability, we first need to calculate both probabilities.
- Theoretical Probability: Tyler believes that a roll of a single 8-sided die indicating a coupon is represented by a roll of 1. The theoretical probability of using a coupon (rolling a 1) is:
\[ P(\text{coupon}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{8} = 0.125 \text{ or } 12.5% \]
- Experimental Probability: From the data provided, 4 out of 48 customers used a coupon. The experimental probability of a customer using a coupon is calculated as follows:
\[ P(\text{coupon, experimental}) = \frac{\text{Number of customers who used a coupon}}{\text{Total number of customers}} = \frac{4}{48} = \frac{1}{12} \approx 0.0833 \text{ or } 8.33% \]
- Comparison:
- Theoretical Probability: 12.5%
- Experimental Probability: 8.33%
Next, we calculate the difference between the two probabilities:
\[ \text{Difference} = P(\text{coupon, theoretical}) - P(\text{coupon, experimental}) = 12.5% - 8.33% \approx 4.17% \]
Now, let's analyze the options based on the calculated probabilities:
- The experimental probability of 8.33% is less than the theoretical probability of 12.5% by approximately 4.17%, which is greater than 2%.
Thus, the correct conclusion is:
The experimental probability is less than the theoretical probability by more than 2%.