Problem:A law school has the following data
It turns out that you would expect a student who scored in the
90th percentile on the LSAT test to be only in the 69th
percentile of the first-year test.
> aveLSAT := 650: sdLSAT := 80: aveFY := 65: sdFY := 8: r := 0.4:
|If someone is in the 69th percentile of the FY test it means that 69 percent of the students scored below this person. Since the FY test scores follow the normal curve we can use the normal TABLE to find out the 69th percentile in standard units. We need to find the z (let's call it z69) that leaves to the left 69% of the area under the normal curve. Since the table only gives areas symmetric about zero, we need to enter the table with the area in between -z69 and z69 i.e. 100%-2*31%=38%. The closest z is,|
> z69 := 0.50:
the value z69=0.50 tells us that the student's score is 0.5 sds
above the ave of first-year test scores. Thus, the regression curve
will predict (0.50)*r = 0.2 standard units for his/her LSAT test.
Using the Normal table again we transform 0.2 SUs to a percentile
in the following way:|