The jury pool for the upcoming murder trial of a celebrity actor contains the na

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?

Great earthquakes off the coast of Oregon have occurred 40 times over the last 10,000 years, ranging in size from magnitude 8.0 to over 9.0. This graph charts these mega-quakes over this period beginning in 8000 BC and shows they occur, on average, about once every 250 years. Evidence found in coastal marshes shows the last great earthquake occured in 1700 AD.

Suppose the probability of a major earthquake on a given year is 40 out of 10,000 years.

A) What is the expected value (or theoretical mean) of a great earthquake off the coast of Oregon in two years?

B) Use the poisson distribution to appropriate the probability that there will be at least one major earthquake in the next two years.

Explanation / Answer

The binomial distribution describes the behavior of a count variable X if the following conditions apply:

1: The number of observations n is fixed.n=12 fixed

2: Each observation is independent. If your select first juror it is not likely to affect others

3: Each observation represents one of two outcomes ("success" or "failure"). Hispanic or not

4: The probability of "success" p is the same for each outcome. p=0.40 for all

So as per binomial distribution Mean=E(x)=np=4.8

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