{"id":"study-empirical-rule-height-math","audience":"high-school","category":"explaining","technique":"examples","track":"study","title":"See the empirical rule worked out with class data","free":false,"task":"Your Statistics class measured heights, and the 68-95-99.7 rule still confuses you. Get exactly 3 numbered lines, one for each percentage, each showing the math for the range like '68%: 65 - 3 = 62 to 65 + 3 = 68 inches', plain text, under 80 words. Use the corrected standard deviation Ms. Lee posted.","materialLabel":"Your stats notes (attached to your prompt automatically)","material":"STATISTICS (regular) - Ms. Lee - Normal distributions\n\nEMPIRICAL RULE (68-95-99.7):\nIn a normal distribution,\n- about 68% of data is within 1 standard deviation (SD) of the mean\n- about 95% is within 2 SDs\n- about 99.7% is within 3 SDs\n\nCLASS DATA: heights of 120 juniors, roughly normal.\nMean = 65 inches\nSD = 4 inches (from the board)\n   ** Ms. Lee (Google Classroom): \"I wrote SD = 4 on the board, but the calculator output says 3. Use SD = 3.\" **\n\nHer tip: \"Write out mean minus and mean plus for each one. Don't just memorize the percentages.\"\n\nMy confusion: what does \"within 2 SDs\" actually mean in inches?\n\nNot on this quiz: z-scores, normalcdf (next week).\nQuiz Monday.","rules":[{"type":"numberedItems","count":3},{"type":"maxWords","max":80},{"type":"plainText"}],"mistakes":[{"title":"Asking for an explanation","why":"The AI restates the rule in words, which you already have.","fix":"Ask for the math: \"Show mean minus and plus for each range.\"","checks":["r0"]},{"title":"Missing the correction","why":"The board's SD and the corrected one are both in your notes.","fix":"Add: \"Use SD = 3 from Ms. Lee's post.\"","checks":["r1"]},{"title":"Not saying how many lines","why":"The AI picks its own number, and it usually picks more lines than you need.","fix":"Be exact: \"Exactly 3 numbered lines.\"","checks":["numberedItems"]},{"title":"Getting next week's topics","why":"The AI may add z-scores or calculator commands.","fix":"Add: \"No z-scores or calculator steps.\"","checks":["r2"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total and it often lands 20% over.","fix":"Cap each line: \"each under 22 words.\"","checks":["maxWords"]},{"title":"Forgetting where it will be read","why":"AI formats for a screen, with bold and headings that show up as stray symbols in your notes.","fix":"Say: \"Plain text, no bold, no headings.\"","checks":["plainText"]}],"promptHints":[{"label":"Asks to show the math","patterns":["show.{0,15}(math|work)","mean (minus|plus)","65 ?- ?3"]},{"label":"Uses the correction","patterns":["sd ?= ?3","correct","3 inches"]},{"label":"Says how many lines","patterns":["\\b(3|three)\\b.{0,25}line"]},{"label":"Rules out extras","patterns":["no z","normalcdf","only"]},{"label":"Sets a length limit","patterns":["\\d+\\s*words","word (limit|count)","under \\d+"]}],"hint":"The rule makes sense once you see the inches. Ask for each range with the subtraction and addition shown, and use the corrected SD.","rubricLabels":["Each line shows the subtraction and addition from the mean for its range, using SD = 3","The ranges are correct: 68% from 62 to 68 inches, 95% from 59 to 71 inches, 99.7% from 56 to 74 inches (none use SD = 4)","No z-scores, normalcdf or extra explanation beyond the 3 lines"]}