Final answer:
The percentage of organs that weigh between 235 grams and 385 grams, based on the given mean and standard deviation, can be determined using the empirical rule. Approximately 99% of the organs will fall within this range.
Step-by-step explanation:
The question asks us to use the empirical rule to determine the percentage of organs that weigh between 235 grams and 385 grams. The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and more than 99% falls within three standard deviations.
In this case, the mean is 310 grams and the standard deviation is 25 grams. To determine the percentage of organs that weigh between 235 grams and 385 grams, we need to find the number of standard deviations these weights are from the mean.
By calculating the z-scores for 235 grams and 385 grams, we can determine the percentage of organs that fall within this range. The z-score is calculated using the formula: (x - mean) / standard deviation.
For 235 grams: (235 - 310) / 25 = -3
For 385 grams: (385 - 310) / 25 = 3
Since the z-score of -3 corresponds roughly to the data falling within three standard deviations below the mean, and the z-score of 3 corresponds to the data falling within three standard deviations above the mean, we know that approximately 99% of the organs will fall within this range.
Therefore, the percentage of organs that weigh between 235 grams and 385 grams is approximately 99%.