According to figures released by the New York City government, smoking among New
ID: 3023013 • Letter: A
Question
According to figures released by the New York City government, smoking among New York City teenagers is on a decline, continuing a trend that began more than a decade ago (The New York Times, January 2, 2008). According to the New York City Youth Risk Behavior Survey, the teenage smoking rate dropped to 8.5% in 2007 from about 17.6% in 2001 and 23% in 1997. City officials attribute the lower smoking rate to factors including a cigarette tax increase, a ban on workplace smoking, and television and subway ads that graphically depict tobacco-related illnesses.
In a report, use the above information to
1. Calculate the probability that at least one in a group of 10 New York City teenagers smoked in 2007.
2. Calculate the probability that at least one in a group of 10 New York City teenagers smoked in 2001.
3. Calculate the probability that at least one in a group of 10 New York City teenagers smoked in 1997.
4. Comment on the smoking trend between 1997 and 2007.
Explanation / Answer
1.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 10
p = the probability of a success = 0.085
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.411349469
Thus, P(at least one) = 1 - P(0) = 0.588650531 [ANSWER]
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2.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 10
p = the probability of a success = 0.176
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.144301922
Thus, P(at least one) = 1 - P(0) = 0.855698078 [ANSWER]
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3.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 10
p = the probability of a success = 0.23
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.073266805
Thus, P(at least one) = 1 - P(0) = 0.926733195 [ANSWER]
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4.
The percentage of teenage smokers in New York City seem to decrease from 1997 to 2007.
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