Question

assume that 12 jurors are randomly selected from a population in which 79% of the people are mexican - americans. refer to the probability distribution table below and find the indicated probabilities.

$x$	$p(x)$
1	0+
2	0+
3	0.0001
4	0.0007
5	0.0044
6	0.0193
7	0.0621
8	0.146
9	0.2442
10	0.2756
11	0.1885
12	0.0591

find the probability of exactly 5 mexican - americans among 12 jurors. round your answer to four decimal places.
$p(x = 5)=$
find the probability of 5 or fewer mexican - americans among 12 jurors. round your answer to four decimal places.
$p(xleq5)=$
does 5 mexican - americans among 12 jurors suggest that the selection process discriminates against mexican - americans?
no
yes

Explanation:

Step1: Find probability of exactly 5

From the table, when \(x = 5\), \(P(x=5)=0.0044\).

Step2: Find probability of 5 or fewer

Sum the probabilities for \(x = 0\) to \(x = 5\). \(P(x\leq5)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=0 + 0+0+0.0001 + 0.0007+0.0044 = 0.0052\)

Step3: Analyze discrimination

The population has 79% Mexican - Americans. The probability of having 5 or fewer Mexican - Americans among 12 jurors (\(P(x\leq5) = 0.0052\)) is very low. This suggests that the selection process discriminates against Mexican - Americans.

Answer:

\(P(x = 5)=0.0044\)
\(P(x\leq5)=0.0052\)
yes