\mu = MEAN and \sigma = STDDEV.
GRADE on the exam.
person(1)'s exam grade was higher than what percentage of test-takers?
Use the cumulative z-table provided below.
A cumulative z-table shows the probability that a standard normal variable will be less than a certain value (z).
In order to use the z-table, we first need to determine the z-score of person( 1 )'s exam grade.
Recall that we can calculate his z-score by subtracting the
mean (\mu) from his
grade and then dividing by the standard deviation
(\sigma).
Recall that we can calculate her z-score by subtracting the
mean (\mu) from her
grade and then dividing by the standard deviation
(\sigma).
\large{\quad z \quad = \quad
\dfrac{x - \pink{\mu}}{\purple{\sigma}}
\quad = \quad \dfrac{GRADE - \pink{MEAN}}{\purple{STDDEV}}
\quad = \quad localeToFixed(ZSCORE, 2)}
Look up localeToFixed(ZSCORE, 2) on the z-table. This value,
localeToFixed(ANSWER, 4), represents
the portion of the population that scored lower than
GRADE on the exam.
person( 1 ) scored higher than
localeToFixed(ANSWER * 100, 2)\% of the
test-takers on the course( 1 ) exam.