Find the Value of a Normal Random Variable

Using Base R

Use the following command to determine the value of a normal random variable that corresponds to a certain proportion, probability, or percentile:

qnorm(percentile, \(\mu\),\(\sigma\))

Recall, the percentile is the area under the normal curve to the left of some value. Let’s find the value of x such that the area under the normal curve to the left of x is 0.75 where \(\mu\) = 100 and \(\sigma\) = 15. That is, we will find the third quartile.

qnorm(0.75,100,15)

## [1] 110.1173

So, the third quartile, \(Q_3\) is 110.1.

Using Mosaic

Install the Mosaic package, if necessary.

install.packages("mosaic")

Use the following command to determine the value of a normal random variable that corresponds to a certain proportion, probability, or percentile:

xqnorm(percentile, \(\mu\),\(\sigma\))

Recall, the percentile is the area under the normal curve to the left of some value. Let’s find the value of x such that the area under the normal curve to the left of x is 0.75 where \(\mu\) = 100 and \(\sigma\) = 15. That is, we will find the third quartile.

library(mosaic)
xqnorm(0.75,mean=100,sd=15)

## [1] 110.1173

So, the third quartile, \(Q_3\) is 110.1.