A highly selective boarding school will only admit students who place at least 1.5 standard deviations above the mean on a standardized test that has a mean of 100 and a standard deviation of 20. what is the minimum score that an applicant must make on the test to be accepted?

The mean is given by:

And the deviation is given by

And for this case we are interested in the minimum score that an applicant must make on the test to be accepted

And we know that the score to be accepted needs to be at least 1.5 deviations above the mean, so we can calculate the minimum score with the following formula:

So then the the minimum score that an applicant must make on the test to be accepted is 130

Step-by-step explanation:

For this case we have the following info:

The mean is given by:

And the deviation is given by

And for this case we are interested in the minimum score that an applicant must make on the test to be accepted

And we know that the score to be accepted needs to be at least 1.5 deviations above the mean, so we can calculate the minimum score with the following formula:

So then the the minimum score that an applicant must make on the test to be accepted is 130

its a straight line parallel to the time axis