Answered: Suppose you are a lawyer representing a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

i need help with this question:
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.

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

Expert Solution

Step 1: Determine the variable

In this case, each of the considered jurors has the only options of "being Hispanic" (defined as success) or "not being Hispanic" (defined as failure). For a considered $n$ juror (the number of trials, $n < \infty$ ), with a defined probability that a juror is Hispanic (i.e., the success probability, $p$ is fixed), the random variable " $X$ as the number of Hispanic jurors" is claimed to follow Binomial distribution.

For $X \sim B (n, p)$ , the PMF is given as follows:

$P (X = x) =^{n} C_{x} p^{x} (1 - p)^{n - x}; x = 0, 1, 2, . . ., n$

$= 0; Otherwise$

For $12$ selected jurors (i.e., $n = 12$ ) with the given probability that a juror is Hispanic, i.e., $p = 60 %$ (or $0.60$ ), the distribution of the random variable is given as: $X \sim B (n = 12, p = 0.60)$ .