Question

A study conducted by three law school professors found that asylum seekers in the United States face broad disparities in the nation’s immigration courts. The professors discovered that 54% of refugees who ask for asylum in the San Francisco immigration court win asylum, but only 12% are granted asylum in the Atlanta immigration court. [Source: Julia Preston, “Wide Disparities Found in Judging of Asylum Cases,” The New York Times, May 31, 2007.]

You randomly select 30 refugees who are asking for asylum in the Atlanta immigration court. Let X denote the number of asylum seekers who win their cases.

The probability that exactly two asylum seekers are granted asylum is 1) .0735 / .1747 / .0844 / .1593  .

The probability that at least five asylum seekers are granted asylum is 2) .2882 / .0827 / .1734 / .1431 .

The expected value of X is 3) 16.2 / 3.6 / 7.5 / 4.8   , and the standard deviation of X is 4) 2.3717 / 2.7298 / 1.7799 / 2.0080 / 3.168

Answer 1

P(Asylum Granted) = P(Refugees who ask for asylum, win asylum)*P(Refugees who win asylum, granted asylum)

P(Asylum Granted) = 0.12

Now, we will be using binnomial distribution to calculate the probability:

Here, Probability of success = 0.12

No. of trials = 30

We have to find the probability that exactly two asylum seekers are granted asylum. So, we need to find P(X = 2)

The probability that exactly two asylum seekers are granted asylum is 0.1747

We have to find the probability that at least five asylum seekers are granted asylum. So , we need to find P(X ≥ 5)

P(X ≥ 5) = 1 - P(X ≤ 4)

So, first we will find P(X ≤ 4)

Thus, P(X ≥ 5) = 1 - P(X ≤ 4) = 1 - 0.7118

P(X ≥ 5) = 0.2882

Since X denote the number of asylum seekers who win their cases. So, p =0.54

The expected value of X = n*p = 30*0.54

The expected value of X = 16.2

Standard deviation = sqrt(n*p*(1-p)) = sqrt(30*0.54*(1-0.54))

Standard deviation = 2.7298