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 )
The grades on an( 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( 1 ) 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 deviationplural( abs( ZSCORE ) ) abovebelow the mean.