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# 二項式機率 BinomialMean <- function(sampleSize, mySuccessProbability) { myMean <- sampleSize * mySuccessProbability myMean } BinomialStdDeviation <- function(sampleSize, mySuccessProbability) { myStdDeviation <- sqrt(sampleSize * mySuccessProbability * (1 - mySuccessProbability)) myStdDeviation } BinomialStdDeviation2 <- function(myMean, mySuccessProbability) { myStdDeviation <- sqrt(myMean * (1 - mySuccessProbability)) myStdDeviation } ############################################################################################## # 隨機選 500 人 sampleSize <- 500 # 完全閱讀保險契約者機率 mySuccessProbability <- 0.44 myMean <- BinomialMean(sampleSize, mySuccessProbability) myStdDeviation <- BinomialStdDeviation2(myMean, mySuccessProbability) # 至多 200 人(含第 200 人),完全閱讀保險契約機率 mySampleSize <- 200.5 myProbability <- pnorm(mySampleSize, mean=myMean, sd=myStdDeviation) print(sprintf("母體閱讀機率=%.4f 樣本平均數=%.4f 當樣本數<=%.1f 時,閱讀機率=%.4f", mySuccessProbability, myMean, mySampleSize, myProbability)) # 完全不閱讀保險契約者機率 mySuccessProbability <- 0.04 myMean <- BinomialMean(sampleSize, mySuccessProbability) myStdDeviation <- BinomialStdDeviation(sampleSize, mySuccessProbability) # 至多 15 人(不含第 15 人),完全不閱讀保險契約機率 mySampleSize <- 14.5 myProbability <- pnorm(mySampleSize, mean=myMean, sd=myStdDeviation) # 至少 15 人(含第 15 人),完全不閱讀保險契約機率 myProbability <- 1 - myProbability print(sprintf("母體不閱讀機率=%.4f 樣本平均數=%.4f 當樣本數>=%.1f 時,不閱讀機率=%.4f", mySuccessProbability, myMean, mySampleSize, myProbability))