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 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 210 grams and 390 ​grams?

​(c) What percentage of organs weighs less than 210 grams or more than 390 ​grams?

​(d) What percentage of organs weighs between 165 grams and 390 ​grams?

Answer 1

The empirical rule is

a) The empirical rule says that

99.7 %of organ lie between 3 standard deviation hence

=300-3*45

=165 and

within 300+ 3*45

=435

b) 210 lies at 300-2*45 at 2 standard deviation and

390 at 300+2*45 at 2 standard deviation

so 95% of organ lie within 210 and 300.

c) Since 95 % of organ lies within 20 and 300 hence by the image above

2.5% of organ lies either less than 210 or above 300.

d) Since 165 lies at -3 standard deviati and 390 lies at 2 standard deviation hence

hence by empirical rule shown ablove

93.35% oegan lies within 165 and 300.