Question

The weight of oranges growing in an orchard is normally distributed with a mean weight of 7 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 68% of all oranges from this orchard.

Answer 1

The weights of the middle 68% of oranges from the orchard will fall between 6 oz. and 8 oz.

Step-by-step explanation:

The weight of oranges growing in an orchard is normally distributed with a mean weight of 7 oz. and a standard deviation of 1 oz. Using the empirical rule, the interval representing weights of the middle 68% of all oranges from this orchard is within one standard deviation of the mean. Therefore, the weights of the middle 68% of the oranges will fall between (mean - standard deviation) and (mean + standard deviation). In this case, the interval will be (7 - 1) oz. to (7 + 1) oz., so the middle 68% of oranges will weigh between 6 oz. and 8 oz.