#Task 1
mean(people$height)
# [1] 179.2391

var(people$height)
# [1] 81.36067

## Standard deviation
sqrt(var(people$height))
# [1] 9.020015
sd(people$height)
# [1] 9.020015

# Stats for the groups
g.means<-aggregate(people$height, 
                   list(people$eye.color,people$sex),
                   mean)
names(g.means)<-names(people)
g.means

g.vars<-aggregate(people$height, 
                   list(people$eye.color,people$sex),
                   var)
names(g.vars)<-names(people)
g.vars

g.sds<-aggregate(people$height, 
                  list(people$eye.color,people$sex),
                  sd)
names(g.sds)<-names(people)
g.sds

install.packages("sciplot")
library(sciplot)

g.ses<-aggregate(people$height, 
                 list(people$eye.color,people$sex),
                 se)
### Task 2
?rnorm
plants<-rnorm(n=10, mean=25.5, sd=2.4)
mean(plants)
# [1] 25.85004

se(plants)
# [1] 0.5452488

var(plants)
# [1] 2.972962

plants.2<-plants
plants.2[5]<-plants.2[5]*10

mean(plants.2)
# [1] 49.74962

se(plants.2)
# [1] 23.98398

var(plants.2)
# [1] 5752.315


median(plants)
# [1] 25.09335
median(plants.2)
# [1] 25.09335


plants.3<-rnorm(n=100, mean=25.5, sd=2.4)
plants.4<-plants.3
plants.4[51]<-plants.4[51]*10

mean(plants.3)
# [1] 25.48203
mean(plants.4)
# [1] 28.10604

### Task 4
bread<-c(100, 105, 95, 115, 110, 105 ,110)
mean(bread)
sd(bread)

### Task A
?pnorm
pnorm(100, 81, 9, lower.tail=F)
# [1] 0.01738138

# Task B
pnorm(50, 81, 9, lower.tail=T)
# [1] 0.0002861171

# Task C
?qnorm
qnorm(0.005, 179, 11, lower.tail = T)
# [1] 150.6659

qnorm(0.005, 179, 11, lower.tail = F)
# [1] 207.3341

# Task D
qnorm(0.05, 179, 11, lower.tail = F)
# [1] 197.0934

# Task E
pnorm(200, 179, 11, lower.tail = F)*550
# [1] 15.46885

# Task F
pnorm(190, 179, 11, lower.tail = T)-
  pnorm(170, 179, 11, lower.tail = T)
# [1] 0.6347181  

# G
qnorm(0.9, 40, sqrt(6), lower.tail = T)
# [1] 43.13915