Question

1. a highly selective boarding school will only admit students who place at least 2 standard deviations above the mean on a standardized test that has a mean of 200 and standard deviation of 26. what is the minimum score that an applicant must make on the test?

Explanation:

Step1: Identify the formula

The formula for a value \(x\) in terms of the mean \(\mu\), standard - deviation \(\sigma\), and z - score \(z\) is \(x=\mu + z\sigma\).

Step2: Determine the values of \(\mu\), \(z\), and \(\sigma\)

We are given that \(\mu = 200\), \(z = 2\) (since students must place at least 2 standard deviations above the mean), and \(\sigma=26\).

Step3: Calculate the minimum score

Substitute the values into the formula: \(x = 200+2\times26\).
First, calculate \(2\times26 = 52\). Then, \(x=200 + 52=252\).

Answer:

252