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Real World
Example #1
Maple tree diameters in a forest area are
normally distributed with mean 10 inches and
standard deviation 2.2 inches. Find the
proportion of trees having a diameter greater
than 15 inches.
Example #2
• White blood cell (WBC) count per cubic
millimeter of whole blood has approximately
the N(7500, 1750) distribution. The lowest 2%
of all WBC counts are defined to be probable
risks. How low must one's WBC count be to fall
in the at-risk group?
Example #3
• The resting heart rate for healthy adult horses
averages 46 beats per minute with a standard
deviation of 8 beats per minute. A horse
whose resting heart rate is in the upper 10% of
the distribution of heart rates may have a
secondary infection or illness that needs to be
treated. How fast must a healthy horse's heart
be beating to fall into this at-risk group?
Example #4
• When robins’ eggs are weighed, it turns out that
they vary according to approximately the normal
distribution with mean 17.5 mg and standard
deviation 3.5 mg.
What proportion of robins’ eggs weigh between 10
mg and 25 mg?
How large are the largest 2% of all robins’ eggs?
Example #5
The length of human pregnancies from conception to birth varies according to a
distribution that is approximately normal with mean 264 days and standard deviation 16
What's the probability a pregnancy lasts less that 250 days?
What's the probability a pregnancy lasts between 240 and 270 days?
Doctors agree that serious thought to labor-inducing procedures ought to accompany any
pregnancy that runs in the longest 2% of all pregnancies. At what day should these
procedures be considered?