Questions: Assume that 12 jurors are randomly selected from a population in which 83% of the people are MexicanAmericans. Refer to the probability distribution table below and find the indicated probabilities. x P(x) 0 0+ 1 0+ 2 0+ 3 0+ 4 0.0002 5 0.0013 6 0.0073 7 0.0305 8 0.0931 9 0.2021 10 0.296 11 0.2627 12 0.1069 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places. P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places. P(x ≤ 7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? yes no

Assume that 12 jurors are randomly selected from a population in which 83% of the people are MexicanAmericans. Refer to the probability distribution table below and find the indicated probabilities. x P(x) 0 0+ 1 0+ 2 0+ 3 0+ 4 0.0002 5 0.0013 6 0.0073 7 0.0305 8 0.0931 9 0.2021 10 0.296 11 0.2627 12 0.1069 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places. P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places. P(x ≤ 7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? yes no
Transcript text: myopenmath.com Math 219/Intersession25 > Assessment Quiz: Chapter 4 59 mins $\times$ Progress saved Score: 3/30 Answered: $1 / 10$ Question 2 Assume that 12 jurors are randomly selected from a population in which $83 \%$ of the people are MexicanAmericans. Refer to the probability distribution table below and find the indicated probabilities. \begin{tabular}{|r|r|} \hline$x$ & $P(x)$ \\ \hline 0 & $0+$ \\ \hline 1 & $0+$ \\ \hline 2 & $0+$ \\ \hline 3 & $0+$ \\ \hline 4 & 0.0002 \\ \hline 5 & 0.0013 \\ \hline 6 & 0.0073 \\ \hline 7 & 0.0305 \\ \hline 8 & 0.0931 \\ \hline 9 & 0.2021 \\ \hline 10 & 0.296 \\ \hline 11 & 0.2627 \\ \hline 12 & 0.1069 \\ \hline \end{tabular} Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places. \[ P(x=7)= \] $\square$ Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places. $P(x \leq 7)=$ $\square$ Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? yes no Question Help: $\triangle$ Message instructor D Post to forum Check Answer
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Solution

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Solution Steps

Step 1: Find the probability of exactly 7 Mexican-Americans among 12 jurors

From the provided probability distribution table, the probability \( P(x=7) \) is given as \( 0.0305 \). Rounding this to four decimal places, we get: \[ P(x=7) = 0.0305 \]

Step 2: Find the probability of 7 or fewer Mexican-Americans among 12 jurors

To find \( P(x \leq 7) \), we sum the probabilities for \( x = 0 \) through \( x = 7 \): \[ P(x \leq 7) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7) \] Substituting the values from the table: \[ P(x \leq 7) = 0 + 0 + 0 + 0 + 0.0002 + 0.0013 + 0.0073 + 0.0305 = 0.0393 \] Rounding to four decimal places: \[ P(x \leq 7) = 0.0393 \]

Step 3: Determine if 7 Mexican-Americans among 12 jurors suggests discrimination

To assess whether 7 Mexican-Americans among 12 jurors suggests discrimination, we compare the observed probability \( P(x=7) = 0.0305 \) with the expected proportion of Mexican-Americans in the population, which is \( 83\% \). Since \( P(x=7) \) is relatively low, it suggests that having exactly 7 Mexican-Americans is less likely than expected. However, without further statistical testing (e.g., hypothesis testing), we cannot definitively conclude discrimination. Thus, the answer is: \[ \text{no} \]

Final Answer

\[ P(x=7) = \boxed{0.0305} \] \[ P(x \leq 7) = \boxed{0.0393} \] The answer is: no.

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