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) = ⁿC_x * p^x * ( 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