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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

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 −

 Live Demo

pnorm(3,mean=1.25,sd=0.75)

Output

[1] 0.9901847