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 20 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 250 grams and 370 grams?

​(c) What percentage of organs weighs less than 250 grams or more than 370 ​grams?

​(d) What percentage of organs weighs between 250 grams and 330 grams?

Answer 1

Given:- mean = 310 grams and standard deviation s = 20 grams

(A) Using empirical rule, we know that 95% of data falls within 2 standard deviation from the mean

95% of data =

(B) we can write 250 as 310 - 3*20 or we can say that 250 is 3 standard deviation below the mean

and we can write 370 as 310 + 3*20 or we can say that 370 is 3 standard deviation above the mean

Using empirical rule, we know that 99.7% of data fall within 3 standard deviation from the mean

so, there is 99.7% data between 250 and 370

(C) Using negation rule of probability

Percentage of data less than 250 and more than 370 = 100- percentage of data between 250 and 370

= 100-99.7

= 0.3%

(D)

we can write 250 as 310 - 3*20 or we can say that 250 is 3 standard deviation below the mean

and we can write 330 as 310 + 1*20 or we can say that 330 is 1 standard deviation above the mean

Using empirical rule, we know that 84% of data fall between 3 standard deviation below and 1 standard deviation above the mean

so, there is 84% data between 250 and 330