Transcript 12.8 Who Takes the GMAT?

Chapter 12
Section 4
Bell Ringer
7.
A public opinion poll in Ohio wants to
determine whether registered voters in the state
approve of a measure to ban smoking in all public
areas. The researchers select a simple random
sample of 50 registered voters from each county in
the state and ask whether they approve or
disapprove of the measure. This is an example of
a.
a systematic county sample.
b.
a stratified sample.
c.
a multistage sample.
d.
a simple random sample.
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 Chapter 12
 Section 4
In general, if all outcomes in a sample space
are equally likely, we find the probability of
any event by
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12.8 Who Takes the GMAT?
In many settings, the “rules of probability” are just basic facts about percents. The Graduate Management
Admission Test (GMAT) website provides the following information about the geographic regions of those who
took the test in 2012–13: 2.3% were from Africa; 0.4% were from Australia and the Pacific Islands; 2.7% were
from Canada; 11.5% were from Central and South Asia; 29.1% were from East and Southeast Asia; 2.1% were
from Eastern Europe; 2.8% were from Mexico, the Caribbean, and Latin America; 3.6% were from the Middle
East; 38.0% were from the United States; and 7.4% were from Western Europe.3
(a)What percent of those who took the test in 2012–13 were from North America (either Canada, the United
States, Mexico, the Caribbean, or Latin America)? Which rule of probability did you use to find the answer?
(b)What percent of those who took the test in 2012–13 were from some other region than the United States?
Which rule of probability did you use to find the answer?
12.9 Overweight?
Although the rules of probability are just basic facts about percents or proportions, we need to
be able to use the language of events and their probabilities. Choose an American adult aged
20 years and over at random. Define two events:
A = the person chosen is obese
B = the person chosen is overweight, but not obese
According to the National Center for Health Statistics, P(A) = 0.36 and P(B) = 0.33.
(a)Explain why events A and B are disjoint.
(b)Say in plain language what the event “A or B” is. What is P(A or B)?
(c)If C is the event that the person chosen has normal weight or less, what is P(C)?
12.10 Languages in Canada.
Canada has two official languages: English and French. Choose a Canadian at random and
ask, “What is your mother tongue?” Here is the distribution of responses, combining many
separate languages from the province of Quebec:
(a)What is the probability that a Canadian’s mother tongue is either English or French?
(b)What probability should replace “?” in the distribution?
(c)What is the probability that a Canadian’s mother tongue is not English?
12.11 Are They Disjoint?
Which of the following pairs of events, A and B, are disjoint? Explain your
answers.
(a)A person is selected at random. A is the event “sex of the person selected is
male” and B is the event “sex of the person selected is female.”
(b)A person is selected at random. A is the event “the person selected earns
more than $100,000 per year” and B is the event “the person selected earns
more than $250,000 per year.”
(c)A pair of dice are tossed. A is the event “one of the dice is a 3” and B is the
event “the sum of the two dice is 3.”