Problems
Find the following probabilities. For problems 1 through 8, z stands for z-score.
1.
2.
3.
4.
5.
6.
7.
8.
z > -2
z < -1
-1 < z < 2
z>2
z>0
z > -1
-3 < z < -2
-1 < z < 3
9. Gina’s doctor told her that the standardized score (z-score) for her systolic
blood pressure, as compare to the blood pressure of other women her age, is
1.50.
a. What is the best interpretation of this standardized score?
b. Probabilities that are less than 2.5% are considered unusual.
Should Gina be concerned about her blood pressure?
10. Esgic(a prescription medication for migraines) has been shown to have a
mean of 650 milligrams (mg) of acetaminophen in each capsule with a
standard deviation of 10 milligrams. Approximately what percent of tablets
would have a mean milligram content of acetaminophen:
a.
b.
c.
d.
greater than 670 milligrams.
between 630 and 640 milligrams.
between 650 and 660 milligrams.
less than 620 milligrams.
11. The number of burglaries in a Princeton community during a given month
has a mean of 4 with a standard deviation of 0.3.
a. Find the probability that more than 4.6 burglaries took place in one
month.
b. Find the probability that less than 3.7 burglaries took place in one month.
12. The monthly electricity consumption of a family dwelling in a 3 bedroom
house has a mean (  ) of 1500 kilowatt-hours with a standard deviation (  )
of 120 kilowatt-hours. If a house is selected at random, find the approximate
probability that the mean energy consumption will:
a. exceed 1860 kilowatt-hours.
b. be between 1140 and 1620 kilowatt-hours.