The weight of an organ in adult males has a bell-shaped distribution with a mean

Question

The weight of an organ in adult males has a bell-shaped distribution with a mean of 340 grams and a standard deviation of 50 grams. Use the empirical rule to determine the following. About 99.7% of organs will between what weights? What percentage of organs weights between 240 grams and 440 grams? What percentage of organs weights less than the 240 grams or more than 440 grams? What percentage of organs weights between 290 grams and 440 grams? ___ and ___ grams (Use ascending order.) ___% (Type an integer or a decimal.) ___% (Type an integer or a decimal.) ___% (Type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation / Answer

(A)

99.7% of the population is covered by 3 sigma level.

Hence lower limit = mean - 3 sigma = 340 - 3*50 = 340 - 150 = 190

upper limit = mean + 3 sigma = 340 + 3*50 = 340 + 150 = 490

i.e. 190 gms to 490 gms

(B)

240 - 340 = 100 and 440 - 340 = 100

This is 2 sigma level i.e. 95% population is covered.

(C)

95% population lies between 240 and 440. This means remaining 5% population is less than 240 and more than 440.

(D)

290 - 340 = -50 i.e. 1 sigma level. Total proportion covered under 1 sigma is 68%. Half of it is 34%.

440 - 340 = 100 i.e. 2 sigma level. Total population covered under 2 sigma is 95%. Half of it is 42.5%

Hence total percentage of organ weights between 290 grms and 440 grms is 34 + 47.5 = 81.5 %

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