The weight of an organ in adult males has a bell-shaped distribution with a mean
ID: 3231399 • Letter: T
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 20 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 280 grams and 320 grams? (c) What percentage of organs weighs less than 280 grams or more than 320 grams? (d) What percentage of organs weighs between 280 grams and 360 grams? (a) and grams (Use ascending order.) (b) % (Type an integer or a decimal) (c) (Type an integer or a decimal.) (d) (Type an integer or decimal rounded to the nearest hundredth as needed.)Explanation / Answer
a) z for 99.7% is 3. thus lower limit is 300-20*3 to 300+20*3 i.e 240 abd 360
b) we see that here z is (320-300)/20 or 1. thus it is between -1 and 1 and thus the answer is 68%
c) 1-68% or 32%
d) upper z is 3 and lower is -1 thus, 99.87-(1-0.8413)= 99.7%
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