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 = 15.6 and standard deviation σ = 3.9. 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 = 999 and standard deviation σ = 190.Jose scores 927 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jose's SAT score

Answer:1321.Step-by-step explanation:We have been given that 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. We are asked to find the score that Abigail must get on the SAT in order to place in the top 8% of all students.Top 8% is equal to 92% or more.Let us find z-score corresponding to 92% or 0.92. Using normal distribution table, we get a z-score equal to 1.41.Now, we will z-score formula to solve for the score as:[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]1.41=\frac{x-1026}{209}[/tex][tex]1.41*209=\frac{x-1026}{209}*209[/tex][tex]294.69=x-1026[/tex][tex]294.69+1026=x-1026+1026[/tex][tex]1320.69=x[/tex][tex]x\approx 1321[/tex]Therefore, Abigail must get a score of 1321 on the SAT in order to place in the top 8% of all students.