The weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 25 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 260 grams and 360 grams?
(c) What percentage of organs weighs less than 260 grams or more than 360 grams?
(d) What percentage of organs weighs between 285 grams and 385 grams?

About 68% of organs will be between 300 grams and 320 grams, about 95% of organs will be About 68% of organs will be between 300 grams and 320 grams, About 68% of organs will be between 300 grams and 320 grams, about 95% of organs will be between 280 grams and 360 grams, the percentage of organs weighs less than 280 grams or more than 360 grams is 5%, and the percentage of organs weighs between 300 grams and 360 grams is 81.5%.

Given :

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.

A) According to the empirical rule, using the values of mean and standard deviation:

\rm \mu-\sigma = 320-20=300 \; gramsμ+σ=320+20=320grams

Therefore, about 68% of organs will be between 300 grams and 320 grams.

B) Again according to the empirical rule, using the values of mean and standard deviation:

\rm \mu-2\times \sigma = 320-40=280 \; gramsμ−2×σ=320−40=280grams

\rm \mu+2\times \sigma = 320+40=360 \; gramsμ+2×σ=320+40=360grams

Therefore, according to the empirical rule, about 95% of organs will be between 280 grams and 360 grams.

C)

The percentage of organs weighs less than 280 grams or more than 360 grams = 100 - (The percentage of organs weighs between 280 grams and 360 grams)

The percentage of organs weighs less than 280 grams or more than 360 grams = 100 - 95 = 5%

D)

The percentage of organs weighs between 300 grams and 360 grams = 0.5 \times× ( percentage of organs weighs between 280 grams and 360 grams + percentage of organs weighs between 300 grams and 320 grams)

The percentage of organs weighs between 300 grams and 360 grams = 0.5 \times× (95 + 68)

So, the percentage of organs weighing between 300 grams and 360 grams is 81.5%.

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95% of organs will be between 280 grams and 360 grams, the percentage of organs weighs less than 280 grams or more than 360 grams is 5%, and the percentage of organs weighs between 300 grams and 360 grams is 81.5%.

Given :

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.

A) According to the empirical rule, using the values of mean and standard deviation:

\rm \mu-\sigma = 320-20=300 \; gramsμ−σ=320−20=300grams

\rm \mu+\sigma = 320+20=320 \; gramsμ+σ=320+20=320grams

Therefore, about 68% of organs will be between 300 grams and 320 grams.

B) Again according to the empirical rule, using the values of mean and standard deviation:

\rm \mu-2\times \sigma = 320-40=280 \; gramsμ−2×σ=320−40=280grams

\rm \mu+2\times \sigma = 320+40=360 \; gramsμ+2×σ=320+40=360grams

Therefore, according to the empirical rule, about 95% of organs will be between 280 grams and 360 grams.

C)

The percentage of organs weighs less than 280 grams or more than 360 grams = 100 - (The percentage of organs weighs between 280 grams and 360 grams)

The percentage of organs weighs less than 280 grams or more than 360 grams = 100 - 95 = 5%

D)

The percentage of organs weighs between 300 grams and 360 grams = 0.5 \times× ( percentage of organs weighs between 280 grams and 360 grams + percentage of organs weighs between 300 grams and 320 grams)

The percentage of organs weighs between 300 grams and 360 grams = 0.5 \times× (95 + 68)

So, the percentage of organs weighing between 300 grams and 360 grams is 81.5%.

For more information, refer to the link given below:

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