Question

tyler believes that an 8 - sided die can be used to predict whether customers at his store will use a coupon when making their purchases, with a roll of 1 indicating a coupon and all other outcomes indicating no coupon. today, 4 of the first 48 customers in the store used a coupon. how does the experimental probability of a customer using a coupon compare to the theoretical probability of tylers die? the experimental probability is greater than the theoretical probability by more than 2%. the experimental probability is less than the theoretical probability by more than 2%. the experimental probability is greater than the theoretical probability, but within 2%. the experimental probability is less than the theoretical probability, but within 2%.

Explanation:

Step1: Calculate theoretical probability

For an 8 - sided die, if a roll of 1 indicates a coupon, the theoretical probability $P_{theo}$ of getting a 1 is $\frac{1}{8}=0.125$ or 12.5%.

Step2: Calculate experimental probability

4 out of 48 customers used a coupon. So the experimental probability $P_{exp}=\frac{4}{48}=\frac{1}{12}\approx0.0833$ or 8.33%.

Step3: Find the difference

The difference between the theoretical and experimental probabilities is $12.5 - 8.33 = 4.17$ percentage points. Since $4.17> 2$, the experimental probability is less than the theoretical probability by more than 2%.

Answer:

The experimental probability is less than the theoretical probability by more than 2%.