pnorm function in R How does the pnorm function in R work?  I mean how it computes  $P(X<10)$ with only the mean and standard deviation given.  Does it work same like $z$-score to compute percentages?
 A: pnorm calculates cumulative distribution function of normal distribution, i.e.
$$ \Pr(X \le x) = F(x) = \frac12\left[1 + \operatorname{erf}\left( \frac{x-\mu}{\sigma\sqrt{2}}\right)\right] $$
where $\mu$ is mean and $\sigma$ is standard deviation. As noted by dsaxton to calculate the probabilities for normally distributed random variable $X$ you need only to know $\mu$ and $\sigma$ parameters and apply the function.
If you are not familiar with those concepts you should read carefully the Wikipedia articles I linked above and you should check some introductory handbook on statistics, e.g. All of Statistics by Larry Wasserman. Harvard University provides online lecture introducing probability theory called Statistics 110: Probability by Joe Blitzstein, it's also a good starting point.
A: Function dnorm gives PDF and pnorm gives CDF.

For example, if you want to find $P(x<2)$ for standard normal distribution (mean=0 and sd=1), you can use pnorm(2), which is $0.977$.
If you want to find $P(1<x<2)$ for a normal distribution with mean=1 and sd=2 you can do pnorm(2,mean=1,sd=2)-pnorm(1,mean=1,sd=2), which is $0.191$
