Question

a) What are the 10th and 90th percentiles of the distribution of disability classifications?

Every veteran who applies for disability compensation is (eventually) evaluated and classified as having some degree of disability from 0% to 100%. (To make things simple, assume that an 11 point scale is used, so that a veteran's degree of disability is one of 0%, 10%, 20%, ..., 90%, or 100%; a veteran judged to have no disability is classified as 0%, and one judged to be completely disabled is classified as 100%.) The figure below, published with the article, shows the percentage of veterans applying for disability benefits classified as having each degree of disability. (For example, 1.5% of veterans are classified as having 100% disability.) The Cost of Serving Of the 1.5 million troops who have served in Iraq and Afghanistan, 566,901 are now veterans. Nearly one in five has been granted disability benefits. Degree of Percentage of disability total claims 100% ] 1.5% 901 0.9 80 7 2.2 70 E 60 50 5.9 40 11.0 30 13.3 15.2 - 17.2 3.5 5.8 23.6

b) If benefits were awarded only to applicants who are at least 80% disabled (i.e., 80% or more disabled), what
percentage of applicants will receive benefits?

c) According to the figure legend, nearly one in five applying veterans is granted disability benefits. At least what
degree of disability is required to be among the most disabled 20% of veterans?

d) Let X be the degree of disability of a randomly selected veteran. What is the probability that X is greater than
0% (i.e., that the veteran has been classified as having some disability)? (Note that degree of disability is
treated as a discrete random variable.)

Answer 1

No. Of troops=1.5 million

No.of veterans=566,901

No.of veteran granted disability=one-fifth of 566,901

a)10 percentile=23.6percent of total disability granted=(23.6×566,901)÷(100×5)=26,757 (approx)

90 percentile=0.9 percent of total disability granted=(0.9×566,901)÷(100×5)=1020(approx)

b)80 percent or more disable applicants=1.5+0.9+2.2=4.6percent of the total disability granted veterans.

c)No.of people being on the most disabled 20 percent=(20×566,901)÷(100×5)=22,676

Up to 60 percent of disability granted veteran forms the 82 percent of total percentage of disability granted veteran.So to be in the category of 20%of most disabled veterans,one has to be at least 60 percent disabled or more as upto 60 percent comes under the 82 percent of total disability granted person,so some percent of 60 percent also comes in this category.

d)one-fifth of total veterans are granted,so to be classified as having some disability is 20 percent of the total veterans population.