Question
Assume that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
0 0+
1 0+
2 0.0001
3 0.0011
4 0.0063
5 0.0246
6 0.0704
7 0.1477
8 0.2261
9 0.246
10 0.1807
11 0.0804
12 0.0164
Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
0.1477
Correct
Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
0.1729
Incorrect
Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
yes
no
0 0+
1 0+
2 0.0001
3 0.0011
4 0.0063
5 0.0246
6 0.0704
7 0.1477
8 0.2261
9 0.246
10 0.1807
11 0.0804
12 0.0164
Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
0.1477
Correct
Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
0.1729
Incorrect
Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
yes
no
Answers
Answered by
GPT-4o mini
To find the probability of 7 or fewer Mexican-Americans among 12 jurors, we can sum up the probabilities of having 0, 1, 2, 3, 4, 5, 6, and 7 Mexican-Americans. From the provided probability distribution:
- P(0) = 0.0000
- P(1) = 0.0000
- P(2) = 0.0001
- P(3) = 0.0011
- P(4) = 0.0063
- P(5) = 0.0246
- P(6) = 0.0704
- P(7) = 0.1477
Now, summing these values gives us:
\[
P(\text{7 or fewer}) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
\]
Substituting the probabilities:
\[
P(\text{7 or fewer}) = 0.0000 + 0.0000 + 0.0001 + 0.0011 + 0.0063 + 0.0246 + 0.0704 + 0.1477
\]
\[
P(\text{7 or fewer}) = 0.2502
\]
Thus, the correct probability of 7 or fewer Mexican-Americans among 12 jurors is:
**P(7 or fewer) = 0.2502**, rounded to four decimal places.
As for whether having 7 Mexican-Americans among 12 jurors suggests that the selection process discriminates against Mexican-Americans, this depends on the expected probability of Mexican-Americans in the jury. Given that 71% of the population is Mexican-American, we would expect around 8.5 jurors to be Mexican-American if we had a larger sample size reflecting the population percentage. Having only 7 would not, by itself, suggest discrimination without further statistical analysis, like hypothesis testing or confidence intervals.
So, the answer would be:
**Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?**
- **No** (without further evidence or analysis).
- P(0) = 0.0000
- P(1) = 0.0000
- P(2) = 0.0001
- P(3) = 0.0011
- P(4) = 0.0063
- P(5) = 0.0246
- P(6) = 0.0704
- P(7) = 0.1477
Now, summing these values gives us:
\[
P(\text{7 or fewer}) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
\]
Substituting the probabilities:
\[
P(\text{7 or fewer}) = 0.0000 + 0.0000 + 0.0001 + 0.0011 + 0.0063 + 0.0246 + 0.0704 + 0.1477
\]
\[
P(\text{7 or fewer}) = 0.2502
\]
Thus, the correct probability of 7 or fewer Mexican-Americans among 12 jurors is:
**P(7 or fewer) = 0.2502**, rounded to four decimal places.
As for whether having 7 Mexican-Americans among 12 jurors suggests that the selection process discriminates against Mexican-Americans, this depends on the expected probability of Mexican-Americans in the jury. Given that 71% of the population is Mexican-American, we would expect around 8.5 jurors to be Mexican-American if we had a larger sample size reflecting the population percentage. Having only 7 would not, by itself, suggest discrimination without further statistical analysis, like hypothesis testing or confidence intervals.
So, the answer would be:
**Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?**
- **No** (without further evidence or analysis).