Wood-Burning Example

Suppose that the amount of wood that I burn per day is approximately normally distributed with a mean of 16 ft\(^3\) and a standard deviation of 4 ft\(^3\). Use this information to answer the questions below.

  • What is an individual?
  • What is the variable and what type of variable is it?
  • On what proportion of days do I burn less than 22 ft\(^3\) of wood?
  • On what proportion of days do I burn more than 15 ft\(^3\) of wood?
  • On what proportion of days do I burn between 11 and 26 ft\(^3\) of wood?
  • What is the amount of wood burned per day such that I burn less than that amount on 10% of the days?
  • What is the amount of wood burned per day such that I burn more than that amount on 20% of the days?
  • What are the most common 50% of amounts of wood burned per day?

Load NCStats Package

library(NCStats)

Forward, Less-Than

( distrib(22,mean=16,sd=4) )

## [1] 0.9331928

Forward, Greater-Than

( distrib(15,mean=16,sd=4,lower.tail=FALSE) )

## [1] 0.5987063

Forward, Between

( ab <- distrib(26,mean=16,sd=4) )

## [1] 0.9937903
( a <- distrib(11,mean=16,sd=4) )

## [1] 0.1056498
ab-a
## [1] 0.8881406

Reverse, Less-Than}

( distrib(0.1,mean=16,sd=4,type="q") )

## [1] 10.87379

Reverse, Greater Than

( distrib(0.20,mean=16,sd=4,type="q",lower.tail=FALSE) )

## [1] 19.36648

Reverse, Between

( distrib(0.25,mean=16,sd=4,type="q") )

## [1] 13.30204
( distrib(0.25,mean=16,sd=4,type="q",lower.tail=FALSE) )

## [1] 18.69796