Download 1 - Collingswood High School

Normal Distribution Practice
For each question, show all relevant work. Be sure to specify your final answer/conclusion.
1) The angiogram is a standard diagnostic test used in clinical medicine to detect stroke in
patients. This test has some risks for the patient, and several noninvasive techniques
have been developed that are hoped to be as effective as the angiogram. One such
method utilizes the measurement of cerebral blood flow (CBF) in the brain, since stroke
patients tend to have lower levels of CBF than normal. Among healthy people, CBF is
normally distributed with mean 75 and standard deviation 17. Patients are classified as
being at risk for stroke if their CBF is below 40. What proportion of normal patients are
classified as being at risk for stroke?
2) 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.
3) White blood cell (WBC) count per cubic millimeter of whole blood has an approximate
normal distribution with mean 7500 and standard deviation 1750. 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?
4) Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The
distribution of intraocular pressure in the general population is approximately normal
with mean 16 mm Hg and standard deviation 3.2 mm Hg. If the normal range for
intraocular pressure is between 10 and 22 mm Hg, then what proportion of the general
population would fall within this range?
5) 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?
Normal Distribution Practice
6) GPAs of freshman biology majors have approximately the normal distribution with mean
2.87 and standard deviation .34. In what range do the middle 90% of all freshman
biology majors’ GPAs lay?
7) The length of elephant pregnancies from conception to birth varies according to a
distribution that is approximately normal with mean 525 days and standard deviation 32
days. Is it unusual for an elephant pregnancy to last more than 600 days?
8) A forest products company claims that the amount of usable lumber in its harvested
trees averages 172 cubic feet with a standard deviation of 12.4 cubic feet. Assume that
these amounts have approximately a normal distribution. What proportion of trees
contain between 175 and 190 cubic feet?
9) The mean cholesterol level in children is 175 mg/dL with standard deviation 35 mg/dL.
Assume this level varies from child to child according to an approximate normal
distribution. What percentage of children have a cholesterol level above 200 mg/dL?
10) Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in
body energy and storage. In healthy Alaskan brown bears, the amount of porphyrin in
the bloodstream (in mg/dL) has approximate normal distribution with mean 47.5 and
standard deviation 12.2. How low are the porphyrin levels for the lowest 3% of all the
bears?