Final answer:
To estimate the percentage of weddings that cost between $7770 and $9229, we can use the Empirical Rule. The estimated percentage is approximately 8.93%.
Step-by-step explanation:
To estimate the percentage of weddings that cost between $7770 and $9229, we can use the Empirical Rule. According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
First, we need to calculate the z-scores for the lower and upper limits of the cost range. The z-score is calculated using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For the lower limit, z = (7770 - 8500) / 715 = -0.1014. For the upper limit, z = (9229 - 8500) / 715 = 0.1021.
Next, we can determine the percentage of data falling within the range by subtracting the cumulative percentage for the lower limit from the cumulative percentage for the upper limit. Using a standard normal distribution table, we find that the cumulative percentage for z = -0.1014 is approximately 45.26% and the cumulative percentage for z = 0.1021 is approximately 54.19%. Therefore, the estimated percentage of weddings that cost between $7770 and $9229 is approximately 54.19% - 45.26% = 8.93%.