Question

a business college decides to accept only the top 10% of the applicants applying. their acceptance is based on performance on an entrance exam. if the mean was 75 and the standard deviation was 10, then what is the minimum score needed to be accepted to the university? 88 84 90 82

Explanation:

Step1: Find the z - score

We want the top 10% of the applicants. So, the area to the left of the z - score is \(1 - 0.10=0.90\).
Using a standard normal table (z - table), the z - score corresponding to an area of 0.90 is approximately \(z = 1.28\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 75\) (mean), \(\sigma = 10\) (standard deviation), and \(z = 1.28\).
We need to solve for \(x\).

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Answer:

88