Question

In 2017, the mean of the total SAT score for Hawaii is 1085 with standard deviation 195 while the mean for Wisconsin is 1291 with standard deviation 178 (Source: National Center for Education Statistics) In that year, both Kimo living in Hawaii and his cousin Kyle living in Wisconsin took the SAT test. Kimo got 1175 and Kyle got 1210. With respect to their own states, who did relatively better on the test? Justify your answer.

Link below is the source.

https://nces.ed.gov/programs/digest/d17/tables/dt17_226.40.asp

Answer 1

for SAT score for Hawaii = x1

mean = 1085

and standard deviation = 195

for SAT score for Wisconsin = x2

mean = 1291

and standard deviation = 178

here  both Kimo living in Hawaii and his cousin Kyle living in Wisconsin took the SAT test. Kimo got 1175 and Kyle got 1210. With respect to their own states, who did relatively better on the test?

that is Kimo is living in Hawaii = x1 = 1175 test marks and

Kyle is living in Wisconsin = x2 = 1210 test marks

we can find out here z score and compare

z score for Kimo = ( x1 - mean ) / standard deviation = (1175 - 1085) / 195 = 0.4615

and

z score for Kyle = (x2 - mean) / standard deviation = (1210 - 1291 ) / 178 = - 0.4550

here Kimo got more z score than compare to the Kyle

that is Kimo is relatively better than the Kyle .