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)*px*(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