Question

The jury pool for the upcoming murder trial of a celebrity actor contains the names of 100,000 individuals in the population who may be called for jury duty. The proportion of the available jurors on the population list who are Hispanic is .40. A jury of size 12 is selected at random from the population list of available jurors. Let X = the number of Hispanics selected to be jurors for this jury.

a. What is the expected number of hispanic jurors being on the jury?
b. What is the expected value (or theoretical mean) of a great earthquake off the coast of Oregon in two years?
c. Use the poisson distribution to appropriate the probability that there will be at least one major earthquake in the next two years.

Answer 1

Following are the solution to the given question:

Explanation:

Have a Spanish Jury possibility
`= 0.40`

Jury member No. to be chosen
`= n= 12`

Hispanic Juror Expected
`= np = 12* 0.40 = 4.8`

The jury group will be constituted by Hispanic Jurors
`4.8`

OR

The binomial distribution defines the behavior of a count variable X, provided:

There are a set number of data points n.

Set
`n=12`

Each perception is independent. This will not affect others if your first juror is selected

One of two results is that each observation ("success" or "failure"). English or not

Each result has the same chance of "success" p. for every
`p=0.40`

Well by the binomial distribution. Mean
`=E(x)=np=4.8`