The weight of an organ in adult males has a bell-shaped distribution with a mean
ID: 3246210 • Letter: T
Question
The weight of an organ in adult males has a bell-shaped distribution with a mean of
310
grams and a standard deviation of
25
grams. Use the empirical rule to determine the following.
(a) About
68
%
of organs will be between what weights?
(b) What percentage of organs weighs between
235
grams and
385
grams?
(c) What percentage of organs weighs less than
235
grams or more than
385
grams?
(d) What percentage of organs weighs between
285
grams and
385
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 the nearest hundredth as needed.)
Enter your answer in each of the answer boxes.
Explanation / Answer
a)
68% of data is within 1 standard deviation
hence weight of organ is in between (310 -25 , 310+25) which between 285 and 335
b)
310 -235 = 75 , which is 3 standard deviation from mean
hence , 99.7% of organs weighs between 235 and 385
c)
from b) 0.03% weighs less than 235 and more than 385
d)
percentage of organs between 285 and 385 =>
since z-distribution is symmetric
34% (68%/2) weighs between 285 and 310 and 49.85% ( 99.7%/2) weighs between 310 and 385
hence
percentage = 34% + 49.85% = 83.85%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.