Question

he weight of an organ in adult males has a​ bell-shaped distribution with a mean of 320 grams and a standard deviation of 45 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 230 grams and 410 ​grams? ​

(c) What percentage of organs weighs less than 230 grams or more than 410 ​grams? ​

(d) What percentage of organs weighs between 275 grams and 455 ​grams?

Answer 1

Given information:

(a)

According to empirical rule, 99.7% data values lies within 3 standard deviations of mean. So required range is

Answer: (185, 455)

(b)

From given information we have

According to empirical rule, 95% data values lies within 2 standard deviations of mean. That is 95% data values lie between (230, 410).

Answer: 95%

(c)

By the complement rule, percentage of organs weights less than 230 grams or more than 410 grams is

100% - 95% = 5%

Answer: 5%

(d)

We have

According to empirical rule, 68% data values lies within 1 standard deviation of mean.

The percentage of weight between 275 and 320 is

68% /2 = 34%

And

so percentage of weight between 320 and 455 is

So required percentage is

34% + 49.85% = 83.85%

Answer: 83.85%