Question

The weight of an organ in adult males has a​ bell-shaped distribution with a mean of 310 grams and a standard deviation of 40 grams. Use the empirical rule to determine the following. ​(a) About 68​% of organs will be between what​ weights? ​(b) What percentage of organs weighs between 190 grams and 430 ​grams? ​(c) What percentage of organs weighs less than 190 grams or more than 430 ​grams? ​(d) What percentage of organs weighs between 190 grams and 350 ​grams?

Answer 1

(a) between 270 grams and 350 grams

(b) 99.7%

(c) 0.3 %

(d) 83.85 %

Explanation:

We have that
`\mu = 310` grams and
`\sigma = 40` grams. We should compute the following figures to use the empirical rule

`\mu + \sigma  = 310 + 40    = 350`

`\mu + 2\sigma = 310 + 2(40) = 390`

`\mu + 3\sigma = 310 + 3(40) = 430`

`\mu - \sigma  = 310 - 40    = 270`

`\mu - 2\sigma = 310 - 2(40) = 230`

`\mu - 3\sigma = 310 - 3(40) = 190`

using the percentages that is shown in the image below we can find that

(a) About 68% of organs will be between 270 grams and 350 grams

(b) 99.7% of organs weights between 190 grams and 430 grams

(c) 0.3% of organs weights less than 190 grams or more than 430 grams

(d) 83.85% of organs weights between 190 grams and 350 grams