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.

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