Question

When applying for a certain college, students can submit either an ACT score or SAT score. In the 2015-2016 school year, ACT scores had a mean score of 20 with a standard deviation of 5.1. In the same year, SAT scores had a mean score of 1060 with a standard deviation of 195. Suppose the following competing applicants apply to the same school and admissions needs to choose the stronger candidate. Mason scored 25 on the ACT Hunter scored 1200 on the SAT Identify who the college should accept based on z-scores. Explain your answer.

Answer 1

Ans:

z score for Mason:

z score=(25-20)/5.1=0.98

z score for Hunter:

z score=(1200-1060)/195=0.72

As, z score for Mason is higher than than the z score for Hunter,so college should accept Mason as stronger candidate.

Answer 2

To determine which candidate the college should accept based on z-scores, we need to standardize the scores of both Mason and Hunter using the respective mean and standard deviation for each test.

For Mason's ACT score of 25: Mason's z-score for the ACT can be calculated using the formula: z = (x - μ) / σ where x is the score, μ is the mean, and σ is the standard deviation.

For the ACT, Mason's z-score would be: z_ACT = (25 - 20) / 5.1 z_ACT ≈ 0.9804

For Hunter's SAT score of 1200: Similarly, Hunter's z-score for the SAT can be calculated as: z_SAT = (x - μ) / σ

For the SAT, Hunter's z-score would be: z_SAT = (1200 - 1060) / 195 z_SAT ≈ 0.7179

Now, comparing the z-scores, a higher z-score indicates a stronger performance relative to the mean.

In this case, Mason has a higher z-score (0.9804) for the ACT compared to Hunter's z-score (0.7179) for the SAT.

Based on the z-scores, the college should accept Mason as the stronger candidate. Mason's ACT score of 25 is relatively higher than the mean ACT score, while Hunter's SAT score of 1200 is not as high relative to the mean SAT score.

However, it's important to note that this decision is solely based on comparing z-scores and does not consider other factors that may be considered in the college admissions process, such as other qualifications, essays, or extracurricular activities.