randRange(0, 9) randRange(0, 9) roundTo(2, randRange(0, 2) + ROW_INDEX / 10 + COL_INDEX / 100) randRange(70, 90) randRange(2, 6) localeToFixed(GRADE - ZSCORE * STDDEV, 2) (function() { var rowNames = []; for(var i = floorTo(0, ZSCORE); i < (floorTo(0, ZSCORE) + 1); i += 0.1) { rowNames.push(localeToFixed(i, 1)); } return rowNames; })() [.00, .01, .02, .03, .04, .05, .06, .07, .08, .09] (function() { var zGrid = []; for (var i = 0; i < ROWS.length; i++) { var zRow = []; for (var j = 0; j < COLUMNS.length; j++) { zRow.push(zScores(roundTo(2, (floorTo(0, ZSCORE) + i / 10 + j / 100) * 100))); } zGrid.push(zRow); } return zGrid; })() ZGRID[ROW_INDEX][COL_INDEX] "z"
The scores on a statewide course(1) exam were normally distributed with `\mu = MEAN` and `\sigma = STDDEV`.
person(1) scored `GRADE` on the exam.

person(1)'s exam grade was higher than what percentage of test-takers?

Use the cumulative z-table provided below.

HEADER localeToFixed(column, 2).substr(1)
row localeToFixed(zgrid, 4)
roundTo(4, ANSWER)

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.

var nth = ":nth-child(" + (COL_INDEX + 2) + ")"; $(".fake_row").eq(ROW_INDEX).find("span").css("background", ORANGE); $(".fake_row span" + nth).css("background", ORANGE); $(".fake_header span" + nth).css("background", ORANGE); $(".fake_row").eq(ROW_INDEX).find("span" + nth).css("background", BLUE);

person( 1 ) scored higher than `localeToFixed(ANSWER * 100, 2)\%` of the test-takers on the course( 1 ) exam.