randRange( 65, 85 ) randRange( 2, 5 ) + randRange( 0, 1 ) * 0.5 randRangeWeighted( roundTo( 0, MEAN - STDDEV * 3 ), min( roundTo( 0, MEAN + STDDEV * 3 ), 100 ), MEAN, 0 ) roundTo( 2, ( GRADE - MEAN ) / STDDEV )

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Try asking yourself questions after you read a solution hint, to make sure you have a deep understanding. For questions from the "What? Why? How?" Understand-Meaning strategy, click on each word below.

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Many students are not sure what to say, or think their answer isn’t good. That is fine, as long as you try to think about the question, by typing or saying the answer to yourself.
The grades on a course( 1 ) midterm at school( 1 ) are normally distributed with \mu = MEAN and \sigma = STDDEV.
person( 1 ) earned an GRADE on the exam.

Find the z-score for person( 1 )'s exam grade. Round to two decimal places.

ZSCORE

A z-score is defined as the number of standard deviations a specific point is away from the mean.

We can calculate the z-score for person( 1 )'s exam grade by subtracting the mean (\mu) from his grade and then dividing by the standard deviation (\sigma).

We can calculate the z-score for person( 1 )'s exam grade by subtracting the mean (\mu) from her grade and then dividing by the standard deviation (\sigma).

\large{\quad z \quad = \quad \dfrac{x - \color{PINK}{\mu}}{\color{GREEN}{\sigma}}}

\large{\quad z \quad = \quad \dfrac{GRADE - \color{PINK}{MEAN}}{\color{GREEN}{STDDEV}}}

\large{\quad z \quad = \quad ZSCORE}

The z-score is ZSCORE. In other words, person( 1 )'s score was abs( ZSCORE ) standard deviation abovebelow the mean.

The z-score is ZSCORE. In other words, person( 1 )'s score was abs( ZSCORE ) standard deviations abovebelow the mean.