Question

The weight of an organ in adult males has a bell shaped distribution with a mean of 300 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following:

a) About 99.7% of organs will be between what 2 weights?

b) What percentage of organs weigh between 260 grams and 340 grams?

c) What percentage of organs weigh less than 260 grams and more than 340 grams?

d) What percentage of organs weigh between 260 grams and 360 grams?

Answer 1

Empirical rule is: 68-95-99.7

This implies that 68% of data lies within one standard deviation from mean, 95% of data lies within two standard deviations from mean and 99.7% of data lies within three standard deviations from mean.

a) about 99.7% data: then we know it lies within 3 standard deviation from mean.

Lower limit = 300 - 3*20 = 240 grams

Upper limit = 300 + 3*20 = 360 grams

So, about 99.7% of organs will be between 240 grams and 360 grams.

b) 260 = 300 - 2*20

340 = 300 + 2*20

So, these are 2 standard deviation from mean. Hence about 95% of organs weight between 360 grams and 340 grams.

c) From part b) we know that 95% of data lies within 260 grams to 340 grams. So, rest of the data lies outside this range.

Hence, about 5% of organs weight less than 260 grams and more than 340 grams.

d) From part b) we know that about 95% of organ weight between 260 grams to 340 grams.

Now, from 340 to 360 part is the part between 2 sd and 3 sd from mean in the right side.

So, data lies between these two =

Here we divided by 2 because 99.7 - 95 part is symmetrically divided into left and right both sides whereas we just need to consider right side.

95 + 2.35 = 97.35%

So, about 97.35% of organs weight lies between 260 grams and 360 grams.

I hope this will help. Thank you.