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AP Statistics
Normal Distributions Review Activity
EX) The army reports that the distribution of head circumference among soldiers is
approximately normal with mean 22.8 inches and standard deviation of 1.1 inches.
a) What is the probability that a randomly selected soldier’s head will have a circumference that
is greater than 23.5 inches?
b) What is the probability that a randomly selected soldier’s head will have a circumference that is between 20
than 23 inches?
c) How many inches in circumference would a soldier’s head be if it were at the 40th percentile?
d) Helmets are mass-produced for all except the smallest 5% and the largest 5%. Soldiers in the smallest and
largest 5% get custom-made helmets. What head sizes get custom-made helmets?
1) Here are the prices (in cents per pound) of bananas from 15 markets surveyed by the U. S. Department of
Agriculture. Are banana prices normally distributed? Justify your answer.
51
52
45
48
53
52
50
49
52
48
43
46
45
42
50
2) A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose the capacity of gas tanks are
normally distributed with mean of 15 gallons and standard deviation of 0.1 gallon.
a) What is the probability that a randomly selected tank will hold at most 14.8 gallons?
b) What is the probability that a randomly selected tank will hold between 14.7 and 15.1 gallons?
c) How many gallons would a tank hold if it were at the 3rd quartile of this distribution?
d) If two gas tanks are independently selected, what is the probability that both tanks hold at most 15 gallons?
3) Suppose that for the population of students at a particular university, the time required to
complete a standardized exam is normally distributed with mean 45 minutes and standard
deviation 5 minutes.
a) If 50 minutes is allowed for the exam, what proportion of students at this university would be unable to finish
in the allotted time?
b) What proportion of students at this university would finish the exam in more than 38 minutes, but less than
48 minutes?
c) How much time should be allowed for the exam if we wanted 90% of the students taking the test to be able to
finish in the allotted time?
d) How much time is required for the fastest 25% of all students to complete the exam?