Question

Fourteen jurors are randomly selected from a population of 3 million residents. Of these 3 million​ residents, it is known that 42​% 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 42​% 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?

​(a) The proportion of the jury described that is from a minority race is_

​(Round to two decimal places as​ needed.)

​(b) The probability that 2 or fewer out of 14 jurors are​ minorities, assuming that the proportion of the population that are minorities is 42​%, is_

​(Round to four decimal places as​ needed.)

​(c) Choose the correct answer below.

A.The number of minorities on the jury is​ reasonable, given the composition of the population from which it came.

B.The number of minorities on the jury is unusually​ high, given the composition of the population from which it came.

C.The number of minorities on the jury is unusually​ low, given the composition of the population from which it came.

D.The number of minorities on the jury is​ impossible, given the composition of the population from which it came.

Answer 1

Answer:

Given,

x = 2

n = 14

Proportion p^ = x/n

= 2/14

= 1/7

= 0.143

b)

To give the probability that 2 or fewer jurors will be​ minorities

p = 0.42

q = 1 - p

= 1 - 0.42

= 0.58

n = 14

Binomial distribution, P(X) = nCx px qn-x

P(x <= 2) = P(0) + P(1) + P(2)

= 14C0*0.42^0*0.58^14 + 14C1*0.42^1*0.58^13 + 14C2*0.42^2*0.58^12

= 0.0005 + 0.0049 + 0.0233

= 0.0287

c)

Here the probability is less than 0.05, so it is unlikely event.

The number of minorities on the jury is unusually​ low, given the composition of the population from which it came.