Question

1, According to an airline, flights on a certain route are on time 75% of the time. Suppose 10

flights are randomly selected and the number of on-time flights is recorded.

(a) Explain why this is a binomial experiment.

(b) Find and interpret the probability that exactly 6 flights are on time.

(c) Find and interpret the probability that fewer than 6 flights are on time.

(d) Find and interpret the probability that at least 6 flights are on time.

(e) Find and interpret the probability that between 4 and 6 flights, inclusive, are on time.

2, Fourteen jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 48% are of a minority race. Of the 14 jurors selected, 2 are minorities.

(a) What proportion of the jury described is from a minority race?

(b) If 14 jurors are randomly selected from a population where 48% are minorities, what is the probability that 2

or fewer jurors will be minorities?

(c) What might the lawyer of a defendant from this minority race argue?

According to an almanac, 70% of adult smokers started smoking before turning 18 years old.

(a) Compute the mean and standard deviation of the random variable X, the number of smokers who started before 18 in 300 trials of the probability experiment.

(b) Interpret the mean.

(c) Would it be unusual to observe 270 smokers who started smoking before turning 18 years old in a random sample of 300 adult smokers? Why?

Answer #1

1)

a)

it is a binomial probability distribution, because there is
fixed number of trials, n=10

only two outcomes are there, success and failure

p=0.75, q = 0.25

trails are independent of each other

b)

Binomial probability is given by

P(X=x) = C(n,x)*p^{x}*(1-p)^{(n-x)} |

P ( X = 6 ) = C(10,6) * 0.75^6 *
(1-0.75)^4 =
0.1460 (answer)

c)

P(fewer than 6) =P(X<6) = P(x=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5 ) = 0.0781

d)

P(at least 6) = 1 - P(fewer than 6) = 1 - 0.0781 = 0.9219

e) P(4≤x≤6) = P(X=4) + P(X=5) + P(X=6) = 0.01622 + 0.05840 + 0.1460 = 0.2206

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