1 Two out of five adult smokers acquired the habit by age 14

1) Two out of five adult smokers acquired the habit by age 14. If 400 smokers are randomly selected, find the probability that 170 or more acquired the habit by age 14.

2)   The mayor of a small town estimates that 35% of the residents in the town favor the construction of a municipal parking lot. If there are 350 people at a town meeting, find the probability that at least 100 favor construction of the parking lot. Based on your answer, is it likely that 100 or more people would favor the parking lot?

Solution

(1) mean=n*p=400*(2/5) =160

standard deviation =sqrt(n*p*(1-p))

=sqrt(400*(2/5)*(3/5))

=9.797959

So the probability is

P(X>170) = P((X-mean)/s >(170-160)/9.797959)

=P(Z>1.02) =0.1539 (from standard normal table)

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(2) mean=n*p=350*0.35 =122.5

standard deviation =sqrt(n*p*(1-p))

=sqrt(350*0.35*(1-0.35))

=8.923284

So the probability is

P(X>=100) = P(Z>(100-122.5)/8.923284)

=P(Z>-2.52) = 0.0059 (from standard normal table)

No, it is not likely that 100 or more people would favor the parking lot