Question

assume that 12 jurors are randomly selected from a population in which 86% of the people are hispanic. refer to the probability distribution table below where x represents the number of hispanic people on the jury. find the indicated probabilities.

x	p(x)
1	0
2	0
3	0
4	0
5	0.0004
6	0.0028
7	0.0148
8	0.0569
9	0.1553
10	0.2863
11	0.3797
12	0.2537

find the probability of exactly 7 hispanic people among 12 jurors.
$p(x = 7) = \underline{\quad\quad}$

find the probability of 7 or fewer hispanic people among 12 jurors.
$p(x \leq 7) = \underline{\quad\quad}$

does 7 hispanic people among 12 jurors suggest that the selection process discriminates against hispanic people? why or why not?

is this an example of a binomial probability distribution? why or why not?

Explanation:

Step1: Find P(x=7) from table

Locate $x=7$ in the table: $P(x=7)=0.0148$

Step2: Calculate P(x≤7)

Sum probabilities for $x=0$ to $x=7$:
$P(x\leq7)=0+0+0+0+0+0.0004+0.0028+0.0148$
$P(x\leq7)=0.0180$

Step3: Evaluate discrimination question

Check if $P(x=7)$ is unusually low (typically <0.05). Since 0.0148 < 0.05, it is an unusual event, suggesting potential discrimination.

Step4: Verify binomial conditions

1. Fixed number of trials (12 jurors selected)
2. Two outcomes: Hispanic or not Hispanic
3. Independent selections (randomly selected)
4. Constant probability of success (86% Hispanic in population)

Answer:

$P(x=7)=0.0148$
$P(x\leq7)=0.0180$
Yes, it suggests discrimination. The probability of getting only 7 Hispanic jurors is very low (0.0148, less than the typical 0.05 threshold for unusual events), which is unlikely to occur by random chance if the selection process was fair.
Yes, this is a binomial probability distribution. It meets all binomial criteria: fixed number of independent trials, two mutually exclusive outcomes, and a constant probability of "success" (selecting a Hispanic person) for each trial.