M3.S.ID.A.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.
Example Problems
The lifespans of foxes in a particular zoo are normally distributed. The average fox lives 11.2 years; the standard deviation is 2.8 years.
Use the empirical rule () to estimate the probability of a fox living less than 19.6 years.
Use the empirical rule () to estimate the probability of a fox living less than 19.6 years.
The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives years; the standard deviation is years.
Use the empirical rule () to estimate the probability of a zebra living longer than years.
Use the empirical rule () to estimate the probability of a zebra living longer than years.
The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives ; the standard deviation is .
Use the empirical rule (68-95-99.7%) to estimate the probability of a tiger living less than .
Use the empirical rule (68-95-99.7%) to estimate the probability of a tiger living less than .
Khan Academy ResourcesBasic normal calculationsEmpirical ruleCalculating z-scoresNormal distribution: Area between two pointsNormal distribution: Area above or below a pointNormal calculations in reverseCalculate percentilesQualitative sense of normal distributionsNormal distribution problems: Empirical ruleCalculating percentileComparing with z-scoresFinding z-score for a percentileStandard normal table for proportion aboveStandard normal table for proportion between valuesStandard normal table for proportion belowZ-score introductionThreshold for low percentile

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