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 the following. (a) About 95% of organs will be between what weights? (b) What percentage of organs weighs between 180 grams and 480 grams? (c) What percentage of organs weighs less than 180 grams or more than 480 grams? (d) What percentage of organs weighs between 280 grams and 480 grams?

a) About 95% of organs will be within 230 and 430 grams.

b) 99.7%

c) 0.3%

d) 83.85%

Step-by-step explanation:

The empirical rule 68-95-99.7 tells us that:

We have a bell shaped distribution (we can assume as approximately normal) with mean of 330 g. and standard deviation of 50 g.

a) This happens for an interval with ±2 standard deviations from the mean.

That is:

About 95% of organs will be within 230 and 430 grams.

b) We can calculate the z-scores for each value to know how many standard deviations are from the mean.

As the values are 3 standard deviations from the mean each, it is expected that 99.7% of the organs weigh between 180 and 480 grams.

c) This is the complementary of the point b.

Then, it is expected that (100-99.7)%=0.3% of the organs weigh less than 180 grams or more than 480 grams.

d) We can calculate the z-scores for each value to know how many standard deviations are from the mean.

Between 280 and 330 there is 68%/2=34% of the data.

Between 330 and 480 there is 99.7%/2=49.85% of the data.

Then, between 280 grams and 480 grams there is (34+49.85)%=83.85% of the data.

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