Question

The midterm exam in Econ 2201 consisting of 50 students was worth 100 points. The top 5 scores were 75, 81, 88, 92, and 94.

Find the 95th percentile of the score distribution.

a. 86.05

b.89.8

c. 90.2

d. 91.05

e. 92

Answer 1

Explanation:

Given that the midterm exam in Econ 2201 consisting of 50 students was worth 100 points. The top 5 scores were 75, 81, 88, 92, and 94.

We have to find the 95th percentile of the score distribution.

For this purpose let us arrange in ascending order

75, 81, 88, 92, 94

We must have 95% below the value we find out so that it would be the 95th percentile

i.e. here 95% means =
`5*95/100 = 4.75`

4.75 entries should be below that entry

We see that 80% entries are below 92 and 100% below 95

To find 95%

For 20 % difference differnce in score = 94-92 =2

Hence for 15% difference difference in score =
`2((15)/(20) )=1.5`

95th percentile= 92+1.5 = 93.5