Question

There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores for more than 1 million students in a recent high school graduating class was roughly normal with mean μ = 20.8 and standard deviation σ = 4.8. SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean μ = 1026 and standard deviation σ = 209.

How well must Abigail do on the SAT in order to place in the top 20% of all students? (Round your answer to the nearest whole number.)

Answer 1

Solution:-

Given that,

mean = = 1026

standard deviation = = 209

Using standard normal table,

P(Z > z) = 20%

= 1 - P(Z < z) = 0.20  

= P(Z < z) = 1 - 0.20

= P(Z < z ) = 0.80

= P(Z < 0.8416 ) = 0.80  

z = 0.8416

Using z-score formula,

x = z * +

x = 0.8416 * 209 + 1026

x = 1201.89

x = 1202