Final answer:
About 95% of organs will weigh between 230 and 430 grams according to the empirical rule, which states that 95% of the data resides within two standard deviations of the mean for a normal distribution.
Step-by-step explanation:
The question asks us to use the empirical rule (also known as the 68-95-99.7 rule) to determine the weight range within which about 95% of organs will fall if the weight of an organ in adult males is normally distributed with a mean of 330 grams and a standard deviation of 50 grams.
According to the empirical rule, 95% of the data falls within two standard deviations of the mean. So, we calculate the range as follows:
- Lower bound = Mean - 2×Standard Deviation
- Lower bound = 330 - 2×50
- Lower bound = 330 - 100
- Lower bound = 230 grams
- Upper bound = Mean + 2×Standard Deviation
- Upper bound = 330 + 2×50
- Upper bound = 330 + 100
- Upper bound = 430 grams
Therefore, about 95% of organs will weigh between 230 and 430 grams, which matches option A.