Assignment 13

1 Question 1

Part A

#i.
pnorm(25.3,25.4,2.8/sqrt(10))

## [1] 0.4550397

#ii.
pnorm(25.3,25.4,2.8/sqrt(25))

## [1] 0.4291371

#iii.
pnorm(25.3,25.4,2.8/sqrt(50))

## [1] 0.4003126

Part B

As n increases, the probability decreases

Part C

curve(dnorm(x,25.4,2.8/sqrt(10)),from=24,to=27,main="PDF",xlab="x",ylab="F(x)",col="blue",ylim=c(0,1))
curve(dnorm(x,25.4,2.8/sqrt(25)),from=24,to=27,col="red",add=TRUE)
curve(dnorm(x,25.4,2.8/sqrt(50)),from=24,to=27,col="green",add=TRUE)

1.1 Question 2

Part A

100*0.05

## [1] 5

Part B

sqrt(5*(0.95))

## [1] 2.179449

Part C

5

## [1] 5

Part D

2.179/sqrt(30)

## [1] 0.3978292

Part E

pbinom(4,100,0.05)

## [1] 0.4359813

Part F

pnorm(4,5,0.3978292)

## [1] 0.005974591