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Trigonometry
Statistics: Z Scores
1. A machine is used to fill cans of cola. The amount of cola dispensed
into each can varies slightly. Suppose the amount of cola dispensed into
the cans is normally distributed with a mean of 12 fluid ounces and a
standard deviation of 0.4 fluid ounces. What is the probability that a
given can will have between 11.5 and 12.6 ounces?
2. Mortgage statistics indicate that the number of years that a new
homeowner will occupy a house before moving or selling is normally
distributed with a mean of 6.3 years and a standard deviation of 2.3
years.
a. Find the probability that a homeowner will sell or move within 3 years
of buying the house?
b. Find the probability that a homeowner will sell or move after 10 years
of buying the house?
3. Tests show that a certain model of a new car averages 36 miles per
gallon on the highway with a standard deviation of 3 miles per gallon.
Find the probability that the car gets:
a. more than 40 miles per gallon.
b. between 34 and 38 miles per gallon.
4. A city’s annual rainfall has a mean of 40 inches and a standard
deviation of 6 inches. Find the probability that the annual rainfall in the
city is:
a. between 34 and 46 inches.
b. less than 28 inches.
5. Listed are the final exam scores for each student in an economics
class: 72, 88, 96, 75, 85, 98, 80, 87, 78, 90, 80, 87, 82, 88, 93, 82, 84,
97, 98, 83.
a. Find the range of the scores.
b. Find Q1, Q2, Q3.
c. What is the interquartile range (IQR)?
d. Are there any outliers?