Question

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

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

X ~ Bin ( n , p)

Where n = 12 , p = 0.75

Binomial probability distribution is

P(X) = nCx * px * ( 1 - p)n-x

a)

P(X = 6) = 12C6 * 0.756 * ( 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)

= 12C0 * 0.750 * ( 1 - 0.75)12 +12C1 * 0.751 * ( 1 - 0.75)11 +12C2 * 0.752 * ( 1 - 0.75)10 +12C3 * 0.753 * ( 1 - 0.75)9

+12C4 * 0.754 * ( 1 - 0.75)8 +12C5 * 0.755* ( 1 - 0.75)7 + 12C6 * 0.756 * ( 1 - 0.75)6

= 0.0544

c)

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