Question

There are two major tests of readiness for college, the ACT and the SAT. ACTscores are reported on a scale from 1 to 36. The distribution of ACT scores isapproximately Normal, with mean of 21.4 and standard deviation of 5.2. SATscores are reported on a scale from 400 to 1600. The distribution of SATscores is approximately Normal, with mean of 1,200 and standard deviation of212. What ACT scores make up the top 10% of all the scores? Round to thenearest whole number.

Answer 1

Any score greater than 28.06004 and lesser than 36

1) Considering that the ACT has a mean of 21.4 and a Standard Deviation of 5.2. Note that the ACT scores from 1 to 36.

2) Since the question refers to the top 10%, we're talking about people whose grades were greater than 90% of the students who took the same ACT test.

3) So, let's look up into the Z-score table and find the

Z-score for 0.9: .1.28077

Now picking the z-score and turning it into a raw score we can write:

`\begin{gathered} z=(X-\mu)/(\sigma) \\ 1.28077=(X-21.4)/(5.2) \\ 6.66004=X-21.4 \\ X=6.66004+21.4 \\ X=28.060004 \end{gathered}`

Thus if somebody takes a note greater than 28.060004 he/she will be in the top 10%