Questions: The weight of an organ in adult males has a bell-shaped distribution with a mean of 320 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following. (a) About 99.7% of organs will be between what weights? (b) What percentage of organs weighs between 300 grams and 340 grams? (c) What percentage of organs weighs less than 300 grams or more than 340 grams? (d) What percentage of organs weighs between 300 grams and 380 grams? (a) and grams (Use ascending order.)

Solution Steps

The empirical rule states that 99.7% of the data in a normal distribution falls within three standard deviations of the mean. Lower bound: mean - 3 * standard deviation = 320 - 3 * 20 = 320 - 60 = 260 grams Upper bound: mean + 3 * standard deviation = 320 + 3 * 20 = 320 + 60 = 380 grams

300 grams is one standard deviation below the mean (320 - 20 = 300). 340 grams is one standard deviation above the mean (320 + 20 = 340). The empirical rule states that 68% of the data falls within one standard deviation of the mean.

Since 68% of the data falls between 300 and 340 grams, the remaining percentage falls outside this range. 100% - 68% = 32%

Final Answer