Question

1) 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 are approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean μ = 1498 and standard deviation σ = 316. Jorge scores 1850 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jorge's SAT score? (Round your answer to one decimal place.)

2)

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 are approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean μ = 1498 and standard deviation σ = 316.

What SAT scores make up the top 13% of all scores? (Round your answer to the nearest whole number.)

Scores and higher make up the top 13% of all scores.

Answer 1

Q.1) Given that,

For ACT scores : mean μ = 21.5 and standard deviation σ = 5.4

For SAT scores : mean μ = 1498 and standard deviation σ = 316

Z-score for SAT score of x = 1850 is,

Z = (X - μ)/σ = (1850 - 1498)/316 = 352/316 = 1.11

We want to find, the ACT score for z = 1.11

X = Zσ + μ = (1.11 * 5.4) + 21.5 = 6.0 + 21.5 = 27.5

Therefore, required ACT score is 27.5

2) We want to find, the SAT scores that make up the top 13% of all scores.

That is to find, the value of x such that, P(X > x) = 0.13

=> P(X > 1855) = 0.13

Therefore, required score is 1855