房仲業務帶客看屋機率計算

場景：

• • 假定某房仲業務在客戶來電中，有平均 25% 客戶願意進一步看屋。

  • 該房仲業務統計某個月來電，假定其標準誤差為 0.0625。

問題：

• • 求算該週有幾通來電。（16）

  • 求算樣本分佈曲線。

• • 求算超過 30% 客戶願意進一步看屋之機率。（0.2119）

GNU R：

# 樣本分佈平均值 SampleDistributionMean <- function(populationMean) { myMean <- populationMean myMean } # 已知母體平均數，樣本數，求算樣本標準差 SampleDistributionStdDeviation <- function(populationStdDeviation, sampleSize) { myStdDeviation <- populationStdDeviation / sqrt(sampleSize) myStdDeviation } # 樣本分佈標準誤差 SampleDistributionStdError <- function(sampleDistributionStdDeviation) { myStdError <- sampleDistributionStdDeviation myStdError } # 已知母體平均數，樣本標準差，求算樣本在某母體平均數百分比區間之機率 SampleDistributionPercentageRangeProbability <- function(populationMean, sampleStdDeviation, samplePercentageRange) { sampleValueRange <- populationMean * samplePercentageRange z2 <- sampleValueRange z1 <- -1 * z2 p2 <- pnorm(z2, sd=sampleStdDeviation) p1 <- pnorm(z1, sd=sampleStdDeviation) myProbability <- p2 - p1 myProbability } # 已知母體平均數，樣本標準差，求算樣本在某母體平均數值區間之機率 SampleDistributionValueRangeProbability <- function(sampleStdDeviation, sampleValueRange) { z2 <- sampleValueRange z1 <- -1 * z2 p2 <- pnorm(z2, sd=sampleStdDeviation) p1 <- pnorm(z1, sd=sampleStdDeviation) myProbability <- p2 - p1 myProbability } # 已知母體平均數，樣本標準差，求算樣本在某母體平均數值區間之機率 SampleDistributionProbability <- function(sampleMean, sampleStdDeviation, sampleValue) { z <- (sampleValue - sampleMean) / sampleStdDeviation myProbability <- pnorm(z) myProbability } PlotNormalDistributionChat <- function(meanValue, stdDeviation) { myChartTitle <- sprintf("平均值=%.2f 標準差=%.4f", meanValue, stdDeviation) curve(main=myChartTitle, exp((-1 * (x - meanValue)^2)/(2 * stdDeviation ^ 2))/(stdDeviation * sqrt(2 * pi)), from=meanValue - 3 * stdDeviation, to=meanValue + 3 * stdDeviation, n=100, xlab="值", ylab="機率密度") myChartTitle } ############################################################################################################## populationMean <- 0.25 sampleStdDeviation <- 0.0625 sampleMean <- SampleDistributionMean(populationMean) sampleSize <- (sampleMean / sampleStdDeviation) ^ 2 print(sprintf("樣本數=%d 平均值=%.2f 標準差=%.4f", round(sampleSize), sampleMean, sampleStdDeviation)) sampleValueRange <- 0.3 myProbability <- 1 - SampleDistributionProbability(sampleMean, sampleStdDeviation, sampleValueRange) print(sprintf("區間>=%.2f 機率=%.4f", sampleValueRange, myProbability)) PlotNormalDistributionChat(sampleMean, sampleStdDeviation)