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The weight of an organ in adult males has a bell-shaped distribution with a mean of 330 grams and a standard deviation of 50 grams. Use the empirical rule to determine about 95% of organs will be between what weights?

A. Between 230 and 430 grams
B. Between 280 and 380 grams
C. Between 330 and 430 grams
D. Between 280 and 430 grams

User Donnikitos
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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.

User Shalan
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