Question

The weight of an organ in adult males has a​ bell-shaped distribution with a mean of 350 grams and a standard deviation of 35 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 280 grams and 420 ​grams? ​(c) What percentage of organs weighs less than 280 grams or more than 420 ​grams? ​(d) What percentage of organs weighs between 245 grams and 385 ​grams?

Answer 1

= mean = 350

= SD = 35

(a) By empirical rule, about 99.7 % of values will lie between 3

Substituting values, we get:

350 ( 3 X 35)

= 350 105

= ( 245, 455)

(b)

To find P(280 < X < 420):
Case 1:
X from 280 to mid value:
Z = (280 - 350)/35 = - 2

Case 2:
X from mid value to 420:
Z = (420 - 350)/35 = 2

By empirical rule, 95% of values will fall between two standard deviations from mean.

So,

Answer is:

95 %

(c)

To find P(x<280):

Z = (280 - 350)/35 = - 2

To find P(X>420):

Z = (420 - 350)/35 = 2

By empircal rule, about 5 % of values will lie outside two stadard deviations from mean.

So,

Answer is:

5 %

(d) To find P(245 < X < 385):
Case 1: X from 245 to mid value:
Z = (245 - 350)/35 = - 3

Case 2: X from mid value to 385:
Z = (385 - 350)/35 = 1

By empirical rule, 99.7/2 = 49.85 % will lie from - 3 to mid value.

By empirical rule, 68/2 = 34 % will lie from mid value to 1 .

Thus, percentage of organs weighs between 245 grams and 385 grams = 49.85 + 34 = 83.85 %