Question

6. Assume that 12 jurors are randomly selected from a population in which 75% 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.

P(x=6)=

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

P(x≤6)=

Does 6 Mexican-Americans among 12 jurors suggest that the selection
process discriminates against Mexican-Americans?

- no
- yes

Answer #1

X ~ Bin ( n , p)

Where n = 12 , p = 0.75

Binomial probability distribution is

P(X) = ^{n}C_{x} * p^{x} * ( 1 -
p)^{n-x}

a)

P(X = 6) = ^{12}C_{6} * 0.75^{6} * ( 1 -
0.75)^{6}

= **0.0401**

b)

P(X <= 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= ^{12}C_{0} * 0.75^{0} * ( 1 -
0.75)^{12} +^{12}C_{1} * 0.75^{1} *
( 1 - 0.75)^{11} +^{12}C_{2} *
0.75^{2} * ( 1 - 0.75)^{10}
+^{12}C_{3} * 0.75^{3} * ( 1 -
0.75)^{9}

+^{12}C_{4} * 0.75^{4} * ( 1 -
0.75)^{8} +^{12}C_{5} * 0.75^{5}* (
1 - 0.75)^{7} + ^{12}C_{6} *
0.75^{6} * ( 1 - 0.75)^{6}

= **0.0544**

c)

**Yes,** Since probability that 6 Mexican-Americans
among 12 jurors is less than 0.05

Assume that 12 jurors are randomly selected from a population in
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xx
P(x)P(x)
0
0+
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