Question

2. Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable x is the number of Mexican-Americans on the jury. x 0 1 2 3 4 5 6 7 8 9 10 11 12 P(x) 0.000 0.003 0.016 0.054 0.121 0.193 0.226 0.193 0.121 0.054 0.016 0.003 0.000 a. Find the probability of exactly 6 Mexican-Americans among 12 jurors. b. Find the probability of 6 or fewer Mexican-Americans among 12 jurors. c. Which probability is relevant for determining whether 6 jurors among 12 is unusually low: the result from part (a) or part (b)? d. Is 6 an unusually low number of Mexican-Americans among 12 jurors

Answer 1

Answer:

a) 0.226

b) 0.613

c) Part(a)

d) Unusual event          

Step-by-step explanation:

We are given the following in the question:

   x:         0             1           2            3           4          5            6            7           8

P(x):    0.000    0.003    0.016     0.054    0.121    0.193    0.226     0.193    0.121  

   x:       9             10          11           12

P(x):   0.054     0.016     0.003    0.000

a)  Probability of exactly 6 Mexican-Americans among 12 jurors.

$P(x = 6) = 0.226$

Thus, 0.226 is the probability of exactly 6 Mexican-Americans among 12 jurors

b) Probability of 6 or fewer Mexican-Americans among 12 jurors

$P(x \leq 6) \\=P(x = 0) + P(x = 1) + P(x =2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)\\= 0.000+0.003+ 0.016 +0.054 +0.121+ 0.193+ 0.226\\=0.613$

Thus, 0.613 is the probability that  6 or fewer Mexican-Americans among 12 jurors.

c) The result from part​ (a), because it measures the probability of exactly  6

successes.

d) Unusual event

An event is said to be unusual if the probability of event is less than 0.5.

Since

$P(x = 6) = 0.226 < 0.5$

Thus, it is an unusual event as the probability is less than 0.5