Question

Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.0005 5 0.0033 6 0.0155 7 0.0532 8 0.1329 9 0.2362 10 0.2835 11 0.2062 12 0.0687

Answer 1

To find the probability of selecting a specific number of Mexican-American jurors from a population where 80% of the people are Mexican-Americans, we can use the Binomial distribution. Let X be the random variable representing the number of Mexican-American jurors selected from the population. Then, the probability mass function (PMF) of X is given by:

P(X = k) = (12C k) (0.8)k (0.2)12-k

where (12C k) is the combination formula that gives the number of ways to choose k Mexican-American jurors from a population of 12 jurors:

(12C k) = 12! / (k! (12 - k)!)

Then, for example, to find the probability of selecting exactly 3 Mexican-American jurors, we would calculate:

(12C 3) (0.8)3 (0.2)9 = 0.0768

Similarly, to find the probability of selecting 4 Mexican-American jurors, we would calculate:

(12C 4) (0.8)4 (0.2)8 = 0.0435

And so on for the other probabilities. Note that the sum of the probabilities for each outcome from 0 to 12 must equal 1.