Question

A study was conducted on students from a particular high school over the last 8 years. The followinginformation was found regarding standardized tests used for college admittance Scores on the SAT test arenormally distributed with a mean of 1030 and a standard deviation of 200. Scores on the ACT test are normallydistributed with a mean of 19 and a standard deviation of 5. It is assumed that the two tests measure the sameaptitude, but use different scales.If a student gets an SAT score that is the 59 percentile, find the actual SAT score,SAT scoreRound answer to a whole numberWhat would be the equivalent ACT score for this student?ACT scoreRound answer to I decimal place,If a student gets an SAT score of 1390, And the equivalent ACT score,ACT score -Round answer to I decimal place.

Answer 1

1) Let's tackle this question by dividing it into two parts.

2) SAT

Note that given that the student gets a score in the 59 percentile, we need to find the corresponding z-score for a probability of 0.59. Resorting to a standard normal table, we can state that:

`Z=0.22754`

Now, let's find the raw score plugging into that the z-score into the Z score formula:

`\begin{gathered} Z=(X-\mu)/(\sigma) \\ 0.22754=(X-1030)/(200) \\ X-1030=45.508 \\ X=1075.58 \end{gathered}`

We still need to round it off to the nearest whole number: 1076

3) ACT

The process will be very similar to the previous one, so let's find the ACT score, considering that