NC.M4.SP.3.3
Recognize from simulations of sampling distributions of sample means and proportions that a normal distribution can be used as an approximate model in certain situations.
Example Problems
A city researcher randomly samples 50 households. Each household independently has a 70% chance of having at least one pet. Let represent the number of households with pets in the sample of 50.
Find the mean of .
Find the mean of .
A coin lands heads with probability on each flip. The coin is flipped 40 times, and flips are independent. Let represent the number of heads observed in the 40 flips.
Find the mean of .
Find the mean of .
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.
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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