Question

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 300 and a standard - deviation of 24. what is the minimum score that an applicant must make on the test to be accepted? the minimum score that an applicant must make on the test to be accepted is

Explanation:

Step1: Recall the formula for z - score related value

The formula to find a value $x$ in a normal - distribution is $x=\mu + z\sigma$, where $\mu$ is the mean, $z$ is the z - score, and $\sigma$ is the standard deviation.

Step2: Identify the values of $\mu$, $z$, and $\sigma$

We are given that $\mu = 300$, $z = 2$ (since students must place at least 2 standard deviations above the mean), and $\sigma=24$.

Step3: Calculate the minimum score $x$

Substitute the values into the formula: $x = 300+2\times24$.
First, calculate $2\times24 = 48$.
Then, $x=300 + 48=348$.

Answer:

348