Question

Twelve jurors are randomly selected from a population of 4 million residents. Of these 4 million​ residents, it is known that 46​% are of a minority race. Of the 12 jurors​ selected, 2 are minorities.
​(a) What proportion of the jury described is from a minority​ race? ​
(b) If 12 jurors are randomly selected from a population where 46​% 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?

Answer 1

Answer:  a) 0.17, b) 0.0363

Step-by-step explanation:

Since we have given that

Number of jurors selected = 12

Number of minorities of jurors = 2

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

$\dfrac{2}{12}=\dfrac{1}{6}=0.166666\approx0.17$

(b) If 12 jurors are randomly selected from a population where 46​% are​ minorities, what is the probability that 2 or fewer jurors will be​ minorities?

Let X be the number of jurors who are minorities.

Probability of getting minorities = 0.46

Probability of getting no minorities = 1-0.46 =0.54

$P(X\leq 2)=^{12}C_0(0.54)^{12}+^{12}C_1(0.46)(0.54)^{11}+^{12}C_2(0.46)^2(0.54)^{10}\\\\P(X\leq 2)=0.0363$

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

Since the number of minorities juror are high among the population.

Hence, a) 0.17, b) 0.0363