Assume that 12 jurors are randomly selected from a population in which 86% 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+
4	0+
5	0.0004
6	0.0028
7	0.0148
8	0.0569
9	0.1553
10	0.2863
11	0.3197
12	0.1637


Find the probability of exactly 6 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
 

Find the probability of 6 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
 

If the the probability of 6 or fewer Mexican-Americans is less than 5% then it is unusual, and suggest that there might be descrmination. Does 6 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
yes
no

Let's break down the problem:

### 1. **Find the probability of exactly 6 Mexican-Americans among 12 jurors.**

From the given probability distribution table, the probability of exactly 6 Mexican-Americans is given as \( P(X = 6) = 0.0028 \).

Thus, the probability is:
\[
P(X = 6) = 0.0028
\]

---

### 2. **Find the probability of 6 or fewer Mexican-Americans among 12 jurors.**

To find the probability of 6 or fewer Mexican-Americans, we need to sum the probabilities from 0 through 6.

Using the values from the table:

\[
P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
\]

From the table:
\[
P(X = 0) = 0, \, P(X = 1) = 0, \, P(X = 2) = 0, \, P(X = 3) = 0, \, P(X = 4) = 0, \, P(X = 5) = 0.0004, \, P(X = 6) = 0.0028
\]

Summing these:
\[
P(X \leq 6) = 0 + 0 + 0 + 0 + 0 + 0.0004 + 0.0028 = 0.0032
\]

Thus, the probability of 6 or fewer Mexican-Americans among 12 jurors is:
\[
P(X \leq 6) = 0.0032
\]

---

### 3. **Does the selection process suggest discrimination?**

If the probability of 6 or fewer Mexican-Americans is less than 5%, then it is considered unusual, which might suggest discrimination.

We found that \( P(X \leq 6) = 0.0032 \), which is less than 5% (or 0.05). Therefore, the probability is quite low, suggesting that the selection process may indeed be discriminatory.

Thus, the answer is:
\[
\text{Yes, it suggests that there might be discrimination.}
\]

---

Do you want further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the results change if the percentage of Mexican-Americans in the population were different?
2. What is the probability of selecting exactly 7 Mexican-Americans from the jury?
3. What is the cumulative probability for more than 7 Mexican-Americans in the jury?
4. How would you compute the mean and standard deviation of this probability distribution?
5. What is the role of binomial distribution in such jury selection problems?

**Tip**: The sum of probabilities in a valid probability distribution should always equal 1.

Assume that 12 jurors are randomly selected from a population in which 86% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.

Find the probability of exactly 6 Mexican-Americans among 12 jurors. Round your answer to four decimal places.

Find the probability of 6 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.

If the probability of 6 or fewer Mexican-Americans is less than 5% then it is unusual, and suggests that there might be discrimination. Does 6 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? Yes/No

Explore how to find the probability of selecting exactly 6 Mexican-Americans from a group of 12 jurors using binomial distribution. Includes cumulative probability calculations and an analysis of potential discrimination in the selection process. Ideal for high school students learning probability concepts.

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