Assume that 12 jurors are selected from a population in which 50% of the people

Question

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)
0.0000.000
0.0030.003
0.0160.016
0.0540.054
0.1210.121
0.1930.193
0.2260.226
0.1930.193
0.1210.121
0.0540.054
0.0160.016
0.0030.003
0.0000.000

a. Find the probability of exactly
88
Mexican-Americans among
1212
jurors.
P(88)equals=nothing
b. Find the probability of
88
or fewer Mexican-Americans among
1212
jurors.
The probability of
88
or fewer Mexican-Americans among
1212
jurors is
nothing.
c. Which probability is relevant for determining whether
88
jurors among
1212
is unusually low: the result from part (a) or part (b)?
A.
The result from part (a), because it measures the probability of exactly
88
successes.
B.
The result from part (b), because it measures the probability of
88
or fewer successes.
d. Is
88
an unusually low number of Mexican-Americans among
1212
jurors? Why or why not?
A.
NoNo,
because the relevant probability is
greater thangreater than
0.050.05.
B.
NoNo,
because the relevant probability is
less than or equal toless than or equal to
0.050.05.
C.
YesYes,
because the relevant probability is
greater thangreater than
0.050.05.
D.
YesYes,
because the relevant probability is
less than or equal toless than or equal to
0.050.05.

Explanation / Answer

a)

P(8) = 0.121 [ANSWER]

***********

b)

P(8 or fewer) = 0.000 + 0.003 + 0.016 + 0.054 + 0.121 + 0.193 + 0.226 + 0.193 + 0.121 = 0.927 [ANSWER]

***********

c)

OPTION B: B. The result from part (b), because it measures the probability of 8 or fewer successes.

************

D)

An event is unusual is P < 0.05 for that event.

Hence,

OPTION A: No, because the relevant probability is greater than 0.05. [answer]

*************

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