is.numeric(data$salary)
class(data$salary)

# mean of salary
mean(data$salary)
mean(data$salary, na.rm=T)
# st. dev of salary 
sd(data$salary, na.rm=T)
hist(data$salary)

boxplot(data$salary, outline = F)

# detect outliers

q1<-quantile(data$salary, 0.25 ,  na.rm=T)
q3<-quantile(data$salary, 0.75,  na.rm=T)

summary(data$salary)

iqr<-q3-q1 
lambda <- 1.5 

lower_bound <- q1 -lambda * iqr 
upper_bound <- q3 +lambda * iqr 

# function to remove outliers 
x<-data$salary
salary_no_out<- x[!x %in% boxplot.stats(x)$out] # distr.  of salary witout outliers 
hist(salary_no_out)

# Estimate density
dens <- density(salary_no_out, na.rm = T)
# Plot density
plot(dens)

qqnorm(salary_no_out)
qqline(salary_no_out, col="red", lwd=2)

# salary mean (no outliers)
mean(salary_no_out, na.rm = T)
# st.dev of salary (without outliers)
sd(salary_no_out, na.rm = T)

# 
mean=1693
sd=369
x<- seq(500, 3000, by=1)
pdf_vals<- dnorm(x,mean, sd )
pdf_df <- data.frame(x, pdf_vals)

plot(pdf_df$pdf_vals)

# P(X>1800)
greater<- pnorm(1800, mean, sd)
1- greater


# P(1500<X<1800)

between <- pnorm(1800,mean, sd )-pnorm(1500,mean, sd )
between 

# p(X<1500) 
lower <- pnorm(1500,mean, sd  )
lower