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A Math Teacher Gives Two Different Tests to Measure Students

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A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 23 and a standard deviation of 5.1. Scores on the second test are normally distributed with a mean of 68 and a standard deviation of 10.4. Assume that the two tests use different scales to measure the same aptitude. If a student scores 28 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)


Definitions:

Choice Overload

A cognitive process in which people struggle to make a decision when faced with many options, potentially leading to decision fatigue.

Postdecision Regret

The feeling of remorse or guilt that occurs after making a decision, particularly if the outcome is negative or not as expected.

Mental Resources

The cognitive and emotional capabilities that an individual can draw upon to handle tasks, stress, and demands in life.

Smartphone Devices

Portable electronic devices with advanced computing capabilities and connectivity options.

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