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To find the probability of 5 or fewer Mexican-Americans among 12 jurors, we will sum the probabilities for \(x = 0\) to \(x = 5\) from the given probability distribution table. Here's the step-by-step approach:

### Step 1: List the probabilities from \( x = 0 \) to \( x = 5 \)

\[
P(0) = 0+
\]
\[
P(1) = 0+
\]
\[
P(2) = 0.0001
\]
\[
P(3) = 0.0011
\]
\[
P(4) = 0.0063
\]
\[
P(5) = 0.0246
\]

### Step 2: Sum these probabilities

\[
P(x \leq 5) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5)
\]
\[
P(x \leq 5) = (0+ + 0+ + 0.0001 + 0.0011 + 0.0063 + 0.0246)
\]
\[
P(x \leq 5) = 0.0321
\]

So, the probability \(P(x \leq 5)\) is **0.0321**.

### Step 3: Evaluate if this suggests discrimination
This probability is **significantly low** (approximately 3.2%). Generally, if a probability is less than 5%, it is considered unusual or rare in statistics. Thus, the occurrence of 5 or fewer Mexican-Americans among 12 jurors does suggest that the selection process might discriminate against Mexican-Americans, so the answer is **yes**.

### Would you like further details or have any questions?

### Here are some follow-up questions:
1. How is a binomial distribution used to model this problem?
2. What does "significantly low" imply in statistical decision-making?
3. How would the probability change if the population percentage were different?
4. What are common thresholds for determining statistical significance?
5. How could this analysis apply to jury selection reform policies?

### Tip:
In probability, values below 5% are often considered "unlikely" and can be used to test hypotheses regarding discrimination or bias.

Find the probability of 5 or fewer Mexican-Americans among 12 jurors and evaluate if this suggests discrimination.

Learn how to calculate the probability of having 5 or fewer Mexican-Americans among 12 jurors using a probability distribution table. The solution explains cumulative probability and evaluates statistical significance based on common thresholds for determining discrimination.

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