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How to find the proportion using normal distribution in R?
To find the proportion using normal distribution in R, we can use pnorm function where we can provide the mean and standard deviation of population along with sample, also the tail position can be set by using lower.tail argument to TRUE or FALSE. Check out the below examples to understand how it can be done.
Example 1
Finding the proportion of values above 55 when sample mean is 50 and standard deviation is 8 −
pnorm(55,mean=50,sd=8,lower.tail=FALSE)
Output
[1] 0.2659855
Example 2
Finding the proportion of values above 60 when sample mean is 50 and standard deviation is 8 −
pnorm(60,mean=50,sd=8,lower.tail=FALSE)
Output
[1] 0.1056498
Example 3
Finding the proportion of values above 70 when sample mean is 50 and standard deviation is 8 −
pnorm(70,mean=50,sd=8,lower.tail=FALSE)
Output
[1] 0.006209665
Example 4
Finding the proportion of values below 55 when sample mean is 50 and standard deviation is 8 −
pnorm(55,mean=50,sd=8)
Output
[1] 0.7340145
Example 5
Finding the proportion of values below 60 when sample mean is 50 and standard deviation is 8 −
pnorm(60,mean=50,sd=8)
Output
[1] 0.8943502
Example 6
Finding the proportion of values below 70 when sample mean is 50 and standard deviation is 8 −
pnorm(70,mean=50,sd=8)
Output
[1] 0.9937903
Example 7
Finding the proportion of values above 2 when sample mean is 1.25 and standard deviation is 0.75 −
pnorm(2,mean=1.25,sd=0.75,lower.tail=FALSE)
Output
[1] 0.1586553
Example 8
Finding the proportion of values above 3 when sample mean is 1.25 and standard deviation is 0.75 −
pnorm(3,mean=1.25,sd=0.75,lower.tail=FALSE)
Output
[1] 0.009815329
Example 9
Finding the proportion of values below 2 when sample mean is 1.25 and standard deviation is 0.75 −
pnorm(2,mean=1.25,sd=0.75)
Output
[1] 0.8413447
Example 10
Finding the proportion of values below 3 when sample mean is 1.25 and standard deviation is 0.75 −
pnorm(3,mean=1.25,sd=0.75)
Output
[1] 0.9901847
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