Final answer:
To determine the interval representing the weights of the middle 99.7% of all oranges from the orchard, use the empirical rule. The interval is 6.5 oz. ± 4.5 oz., which is from 2 oz. to 11 oz.
Step-by-step explanation:
To determine the interval that represents weights of the middle 99.7% of all oranges from the orchard, we can use the empirical rule. According to this rule, for a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.
In this case, the mean weight of the oranges is 6.5 oz. with a standard deviation of 1.5 oz. So, we need to find the interval that represents the weights within 3 standard deviations of the mean.
3 standard deviations = 3 * 1.5 oz. = 4.5 oz.
The interval that represents the weights of the middle 99.7% of all oranges from this orchard is 6.5 oz. ± 4.5 oz., which is from 2 oz. to 11 oz.