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Bernoulli and Normal Model Selection worksheets

Distinguish Bernoulli from binomial counts and identify normal support, PDF parameters, variance, and standard deviation.

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Identify the random variable and parameters before calculating. Distinguish a normal variance from its standard deviation.

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Learning objective

What this activity builds

Select an appropriate elementary probability model and interpret its parameters before calculating.

Worked example

One trial succeeds with probability 0.4. Name the model.

Bernoulli(0.4).

A Bernoulli variable records one binary trial; a binomial variable counts several.

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  • State whether one trial or a fixed count is observed.
  • Read N(mu,sigma squared) carefully.
  • Check whether a continuous bell-shaped model is plausible.

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Math SheetNameScoreTeacherDateBernoulli and Normal Model SelectionIdentify the random variable and parameters before calculating. Distinguish a normal variance from its standard deviation.1.X is Bernoulli with P(X=1)=0.2. Find its PMF, F(-1), mean, and variance.Reference: For Bernoulli(p), P(X=1)=p, P(X=0)=1-p, E(X)=p, and Var(X)=p(1-p).2.A model is written X ~ N(6, 2^2), where the second slot is the variance. State the support, mean, variance, standard deviation, and PDF.Reference: For N(mu,sigma^2), support is all real numbers and f(x)=[1/(sigma sqrt(2pi))] exp[-(x-mu)^2/(2sigma^2)].State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateBernoulli and Normal Model SelectionIdentify the random variable and parameters before calculating. Distinguish a normal variance from its standard deviation.3.A measurement is continuous, roughly symmetric and bell-shaped with center 7 and standard deviation 3; let X be one measurement. Is a normal modelsuitable? If so, standardize x=7.Reference: A normal model is plausible for an unbounded-looking continuous bell-shaped measurement without strong skew or discrete counts. Standardize z=(x-mu)/sigma.4.In inspection batch 4, 12 independent components each pass with probability 0.65. Let X count passes. Choose Bernoulli or binomial and state its parameters.Reference: Bernoulli records one binary trial. Binomial counts successes in a fixed number n of independent trials with common p.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateBernoulli and Normal Model SelectionIdentify the random variable and parameters before calculating. Distinguish a normal variance from its standard deviation.5.In inspection batch 5, a randomly selected component either passes or fails, with pass probability 0.8. Define X=1 for pass and 0 for fail. Choose Bernoulli orbinomial and state its parameter.Reference: Bernoulli records one binary trial. Binomial counts successes in a fixed number n of independent trials with common p.6.X is Bernoulli with P(X=1)=0.2. Find its PMF, F(1), mean, and variance.Reference: For Bernoulli(p), P(X=1)=p, P(X=0)=1-p, E(X)=p, and Var(X)=p(1-p).State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateBernoulli and Normal Model SelectionIdentify the random variable and parameters before calculating. Distinguish a normal variance from its standard deviation.7.A measurement is continuous, roughly symmetric and bell-shaped with center 0 and standard deviation 2; let X be one measurement. Is a normal modelsuitable? If so, standardize x=-2.Reference: A normal model is plausible for an unbounded-looking continuous bell-shaped measurement without strong skew or discrete counts. Standardize z=(x-mu)/sigma.8.A model is written X ~ N(1, 3^2), where the second slot is the variance. State the support, mean, variance, standard deviation, and PDF.Reference: For N(mu,sigma^2), support is all real numbers and f(x)=[1/(sigma sqrt(2pi))] exp[-(x-mu)^2/(2sigma^2)].State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 4 of 4

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