學雜費機率計算

場景：

• • 假定美國大學平均學雜費為 $4260 元，標準差為 $900 元。

  • 假定隨機抽樣 50 所大學。

問題：

• • 計算抽樣標準差。（抽樣平均值=4260 抽樣標準差=127.2792）

  • 計算抽樣平均學雜費在 $250 元內之機率。（0.9505）

  • 計算抽樣平均學雜費在 $100 元內之機率。（0.5679）

GNU R：

# Sampling Distibution SamplingDistributionMean <- function(populationMean) { myMean <- populationMean myMean } SamplingDistributionStdDeviation <- function(populationStdDeviation, sampleSize) { myStdDeviation <- populationStdDeviation / sqrt(sampleSize) myStdDeviation } SamplingDistributionStdDeviationInFinitePopulation <- function(populationSize, populationStdDeviation, sampleSize) { myStdDeviation <- sqrt((populationSize - sampleSize) / (populationSize - 1)) * (populationStdDeviation / sqrt(sampleSize)) myStdDeviation } # 常態分配區間機率 NormalDistributionRangedProbaibility <- function(stdDeviation, m, n) { realBigger <- m if (m < n) { realBigger <- n n <- m m <- realBigger } z2 <- m / stdDeviation p2 <- pnorm(z2) z1 <- n / stdDeviation p1 <- pnorm(z1) myProbability <- p2 - p1 myProbability } ############################################################################################################################ populationMean <- 4260 populationStdDeviation <- 900 sampleSize <- 50 myStdDeviation <- SamplingDistributionStdDeviation(populationStdDeviation, sampleSize) print(sprintf("抽樣平均值=%d 抽樣標準差=%.4f", SamplingDistributionMean(populationMean), myStdDeviation)) myProbability <- NormalDistributionRangedProbaibility(myStdDeviation, 250, -250) print(sprintf("抽樣機率=%.4f", myProbability)) myProbability <- NormalDistributionRangedProbaibility(myStdDeviation, 100, -100) print(sprintf("抽樣機率=%.4f", myProbability))