Question

The 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 275 grams and 365 ?grams? ?(c) What percentage of organs weighs less than 275 grams or more than 365 ?grams? ?(d) What percentage of organs weighs between 185 grams and 365 ?grams? ?(a) nothing and nothing grams ?(Use ascending? order.) ?(b) nothing?% ?(Type an integer or a? decimal.) ?(c) nothing?% ?(Type an integer or a? decimal.) ?(d) nothing?% ?(Type an integer or decimal rounded to two decimal places as? needed.)

Answer 1

A) 99.7% of organs will be between 3 standard deviation from the mean.

320 - 3 * 45 = 185

320 + 3 * 45 = 455

So 99.7% of organs will be between 185 and 455.

B) 275 grams and 365 grams are one standard deviation from the mean.

According to the emperical rule about 68% data falls within one standard deviation from the mean.

So 68% of organs weighs between 275 grams and 360 grams.

C) Since 68% of organs weighs between 275 and 360 grams, so 32% of organs weighs less than 275 or more than 360 grams.

D) 185 is 3 standard deviation below the mean and 365 is one standard deviation above the mean.

So 99.7%/2 = 49.85% of organs weighs between the mean and 185 grams.

68%/2 = 34% of organs weighs between the mran and 365 grams.

So total = 49.85% + 34% = 83.85% of organs weighs between 185 grams and 365 grams.