Question

In: Statistics and Probability

Suppose you are a lawyer representing a Hispanic individual in a criminal trial. Twelve jurors are...


Suppose you are a lawyer representing a Hispanic individual in a criminal trial. Twelve jurors are randomly selected by the state from a population that you know to be 60% Hispanic. a. How many jurors would you expect to be Hispanic?

b. The select process produces a jury with 1 Hispanic individuals What proportion of the jury is Hispanic? (Enter your answer as a decimal, rounded to four decimal places)

c. Use the binomial distribution and find the probability that 1 or fewer jurors would be Hispanic.

d. Create a graph of the distribution with the area corresponding to the previous answer shaded in. Choices for creating a graph include: Excel, Binomial Distribution Calculator (in resources menu), TI-84 (take a pic), hand drawn, other software, websites. Upload your finished graph below.

Solutions

Expert Solution

Result:

Suppose you are a lawyer representing a Hispanic individual in a criminal trial. Twelve jurors are randomly selected by the state from a population that you know to be 60% Hispanic.

  1. How many jurors would you expect to be Hispanic?

    n=12, p=0.60

Expected value = n*p=12*0.60 =7.2

Or

7( rounded).

b. The select process produces a jury with 1 Hispanic individuals What proportion of the jury is Hispanic? (Enter your answer as a decimal, rounded to four decimal places)
P=0.0003

Binomial Probabilities

Data

Sample size

12

Probability of an event of interest

0.6

Statistics

Mean

7.2

Variance

2.8800

Standard deviation

1.6971

Binomial Probabilities Table

X

P(X)

0

0.0000

1

0.0003

2

0.0025

3

0.0125

4

0.0420

5

0.1009

6

0.1766

7

0.2270

8

0.2128

9

0.1419

10

0.0639

11

0.0174

12

0.0022

  1. Use the binomial distribution and find the probability that 1 or fewer jurors would be Hispanic.

    P( x ?1) =P( x=0)+P( x=1) =0.0000+0.0003 = 0.0003

d. Create a graph of the distribution with the area corresponding to the previous answer shaded in. Choices for creating a graph include: Excel, Binomial Distribution Calculator (in resources menu), TI-84 (take a pic), hand drawn, other software, websites. Upload your finished graph below.


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