The weight of oranges growing in an orchard is normally distributed with a mean weight of 5.5 and a standard deviation of 0.5 oz. Using the empirical rule, what percentage of the oranges from the orchard weigh between 5 and 6 oz?
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.
In this case, the mean weight of the oranges is 5.5 oz and the standard deviation is 0.5 oz.
To find the percentage of oranges that weigh between 5 and 6 oz, we need to find out how many standard deviations these weights are from the mean.
5 oz is 0.5 standard deviations below the mean (5 - 5.5 = -0.5), and 6 oz is 0.5 standard deviations above the mean (6 - 5.5 = 0.5).
Since this weight range is within one standard deviation from the mean (-0.5 to 0.5), using the empirical rule, we can expect approximately 68% of the oranges to weigh between 5 and 6 oz.