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%.
For more information, refer to the link given below:
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:
