cumulative log-normal function does not return a correct probability

Question

I have some positive numbers and I am using log-normal distribution to plot and show the probability of CNT being between 1 and 50. I want to color the area below the curve and calculate the probability. I have plotted the chart successfully and I am trying to calculate the probability, however the result being returned does not look right, where am I making a mistake? How can I paint the area below the curve between lb and ub?

    df <-structure(list(Year_Month = structure(1:35, .Label = c("2015-05", 
    "2015-10", "2015-11", "2015-12", "2016-01", "2016-02", "2016-03", 
    "2016-04", "2016-05", "2016-06", "2016-07", "2016-08", "2016-09", 
    "2016-10", "2016-11", "2016-12", "2017-01", "2017-02", "2017-03", 
    "2017-04", "2017-05", "2017-06", "2017-07", "2017-08", "2017-09", 
    "2017-10", "2017-11", "2017-12", "2018-01", "2018-02", "2018-03", 
    "2018-04", "2018-05", "2018-06", "2018-07"), class = "factor"), 
    CNT = c(1, 1, 1, 5, 6, 5, 21, 10, 11, 16, 
    14, 19, 11, 9, 15, 6, 7, 33, 24, 47, 76, 92, 
    72, 92, 63, 60, 69, 66, 65, 89, 91, 76, 84, 71, 
    40)), .Names = c("Year_Month", "CNT"), row.names = c(NA, 
    35), class = "data.frame")


    std=sd(df$CNT)
    m=mean(df$CNT)
    lb=1
    ub=50

    ggplot(df, aes(x=CNT)) +  stat_function(fun=dlnorm, args=list(mean=m, sd=std)) 

    i <- CNT >= lb & CNT <= ub
    area <- plnorm(ub, m, std) - plnorm(lb, m, std)
    area

Answer 1

The parameterization of the log-norm expects you to pass in the mean log value, not the raw value. Try

std <- sd(log(df$CNT))
m <- mean(log(df$CNT))
lb <- 1
ub <- 50

ggplot(df, aes(x=CNT)) +  
  stat_function(fun=dlnorm, args=list(mean=m, sd=std)) + 
  stat_function(fun=dlnorm, args=list(mean=m, sd=std), xlim=c(lb, ub), geom="area") 

plnorm(ub, m, std) - plnorm(lb, m, std)
# [1] 0.7230461