[R] Calculating confidence in an estimate including number of trials?

[Zembower, Kevin]

[Yes, this is related to a homework problem, but is not the problems
itself.]

In my mathematical statistics class, we've just learned about properties
of estimators, and I can now solve manually problems like this:

A sample of size n = 16 is drawn from a normal distribution where sigma
= 10 but mu is unknown. If mu = 20, what is the probability that the
estimator mu hat = Y bar will lie between 10.0 and 21.0?[1]

I solved this by converting to Z scores and using a table of cumulative
values under the normal curve and got an answer of .3108 (someone please
tell me if I'm wrong).

Now I'd like to know how to use R to solve this type of problem. In all
my other problems using normal curves, I used dnorm or pnorm, but
neither of these includes anything regarding the number of trials. I can
put the math into R after I've worked out the equation, but I wondered
if there was an R function that computed this directly, in the same
fashion that pnorm can compute probabilities using parameters of mean
and sd.

Using help.search for 'estimator' or 'sample mean' didn't turn up
anything that I recognized. Any hints on where to go looking for this?

Thanks for your help and advice.

-Kevin

Kevin Zembower
Internet Services Group manager
Center for Communication Programs
Bloomberg School of Public Health
Johns Hopkins University
111 Market Place, Suite 310
Baltimore, Maryland  21202
410-659-6139 

[1] Introduction to Mathematical Statistics and its applications, Larsen
and Marx, fourth ed., question 5.4.4.