Question

The weight of an organ in adult males has a​ bell-shaped distribution with a mean of 325 grams and a standard deviation of 25 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 275 grams and 375 ​grams? ​(c) What percentage of organs weighs less than 275 grams or more than 375 ​grams? ​(d) What percentage of organs weighs between 300 grams and 400 ​grams?

Answer 1

Answer:

(a) between 300 grams and 350 grams  (b) 95%  (c) 5%  (d) 83.85%

Step-by-step explanation:

We have that $\mu = 325$ grams and $\sigma = 25$ grams. Let's compute the following figures to use the empirical rule

$\mu + \sigma  = 325 + 25    = 350$  

$\mu + 2\sigma = 325 + 2(25) = 375$  

$\mu + 3\sigma = 325 + 3(25) = 400$  

$\mu - \sigma  = 325 - 25    = 300$  

$\mu - 2\sigma = 325 - 2(25) = 275$  

$\mu - 3\sigma = 325 - 3(25) = 250$  

using the image below that was made it with help of the empirical rule we find the next figures

(a) About 68% of organs will be between 300 grams and 350 grams

(b) 95% of organs weights between 275 grams and 375 grams

(c) 5% of organs weights less than 275 grams or more than 375 grams

(d) 83.85% of organs weights between 300 grams and 400 grams