Q:

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?

Accepted Solution

A:
Answer:  a) 0.17, b) 0.0363 Step-by-step explanation:Since we have given that Number of jurors selected = 12Number of minorities of jurors = 2​(a) What proportion of the jury described is from a minority​ race? ​ [tex]\dfrac{2}{12}=\dfrac{1}{6}=0.166666\approx0.17[/tex](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 = 0.46Probability of getting no minorities = 1-0.46 =0.54[tex]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[/tex](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