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The Bell Curve: Probability & Statistics: Uncharted

Courses Probability & StatisticsThe Bell Curve

The Bell Curve

Read normal shapes, standardize values, and explain why sums and averages become steady.

Probability & Statistics
Unit 7 of 12
20 lessons
158 min
420 XP

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Lessons

20 total

1The Shape That Keeps Showing UpRecognize the center-heavy, symmetric outline of a normal distribution.InteractiveConcept7 min20 XPOpen
2Middle Heavy, Tail LightMark the one-standard-deviation central region of a bell curve.InteractiveConcept8 min20 XPOpen
3The 68-95-99.7 RuleRecall the approximate normal area within one, two, and three standard deviations.InteractiveConcept8 min20 XPOpen
4Rule WorkoutApply the empirical rule to central regions and symmetric tails.InteractivePractice9 min20 XPOpen
5How Many SDs AwayCompute a z-score as signed distance in standard-deviation units.InteractiveConcept8 min20 XPOpen
6Z WorkoutStandardize raw values across varied centers and spreads.InteractivePractice9 min20 XPOpen
7Compare Across ScalesUse z-scores to compare standing on different testing scales.InteractiveConcept8 min20 XPOpen
8Unusual or NotUse the two-standard-deviation convention as a screening rule.InteractiveConcept7 min20 XPOpen
9Grading on a CurveIdentify class scores more than one standard deviation above the mean.InteractiveConcept7 min20 XPOpen
10Percentiles Meet ZEstimate a percentile from a z-score using the empirical rule.InteractiveConcept8 min20 XPOpen
11Many Small CausesExplain why sums of many small independent effects often cluster near a center.InteractiveConcept7 min20 XPOpen
12Averages Calm DownCompare the spread of sample means as sample size grows.InteractiveConcept7 min20 XPOpen
13The Root-n RuleCalculate how averaging reduces standard deviation by the square root of sample size.InteractiveConcept8 min20 XPOpen
14Not Everything Is NormalIdentify clear violations of a normal-shape model.InteractiveConcept7 min20 XPOpen
15Fat Tails BiteExplain why a normal model can understate extreme-event risk.InteractiveConcept7 min20 XPOpen
16Z Workout IIUse signed z-scores to compare and classify values.InteractivePractice9 min20 XPOpen
17The Quality LineEstimate the share of normally distributed output outside tolerance lines.InteractiveConcept8 min20 XPOpen
18Normal WorkoutCombine empirical-rule areas, z-scores, and root-n spread.InteractivePractice9 min20 XPOpen
19Bell Curve AbuseDetect conclusions that a normal model does not justify.InteractiveConcept7 min20 XPOpen
20Normal Mastery CheckCombine standardized distance, normal shape, and sample-mean spread.InteractiveMastery check10 min40 XPOpen

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