Normal Distributions

The command pnorm can be used to compute the proportion of a standard normal distribution that is below 0.5:

pnorm(0.5)

One way to compute the proportion of a normal distribution with mean 76 and standard deviation 10 that is below 80 is to compute the $z$ score $z = (80 - 76)/10 = 0.4$ and then use pnorm to find the proportion of a standard normal distribution that is below $z= 0.4$:

pnorm((80-76)/10)

An alternative is to give the pnorm the mean and standard deviation to use as additional arguments:

pnorm(80, mean = 76, sd = 10) help(pnorm)

Percentiles of the standard normal distribution are computed with qnorm. The 80th percentile is computed by

qnorm(0.8)

The 80th percentile of a normal distribution with mean 76 and standard deviation 10 can be found by computing the $z$ score, the 80th percentile of the standard normal distribution, and converting the $z$ score back to the original units:

76+10*qnorm(0.8)

Again, an alternative is to give qnorm the mean and standard deviation to use:

qnorm(0.8, mean = 76, sd = 10)

Try some examples of your own in the work area below.

Work Area

Enter your own commands here; then click the Submit button.