Normal Distribution Quantiles

Sounds like homework, which is not an encouraged use of the Rhelp
list. You can either do it in theory...

It is _from_ a homework but I have the solution already (explicitly got 
that done first!) - this was the pasted Latex code (apologies for that, 
but in plain text it looks unreadable[1], and I thought everybody here 
has his / her favorite Latrex editor open all the time anyway...). I'm 
just looking, for my own advancement and programming training, for a way 
of doing that in R - which, from your and Dennis' reply, doesn't seem to 
exist.

I would _not_ misuse the list for getting homework done easily, I will not ask "learning statistics" questions here, and I will always try to find the solution myself before posting something here, I promise!

Thanks anyway for the simulation advice,
Rainer


   (4000 - (40*n))   -329
[1] --------------- = ----
             1        200
      (10*(n^-))
             2




On Saturday 08 January 2011 14:56:20 you wrote:

On Jan 8, 2011, at 6:56 AM, Rainer Schuermann wrote:

This is probably embarrassingly basic, but I have spent quite a few
hours in Google and RSeek without getting a clue - probably I'm
asking the wrong questions...

There is this guy who has decided to walk through Australia, a total
distance of 4000 km. His daily portion (mean) is 40km with an sd of
10 km. I want to calculate the number of days it takes to arrive
with 80, 90, 95, 99% probability.
I know how to do this manually, eg. for 95%
$\Phi \left( \frac{4000-40n}{10 \sqrt{n}}  \right) \leq 0.05$
find the z score...

but how would I do this in R? Not qnorm(), but what is it?

Sounds like homework, which is not an encouraged use of the Rhelp
list. You can either do it in theory or you can simulate it. Here's a
small step toward a simulation approach.

cumsum(rnorm(100, mean=40, sd=10))

   [1]   41.90617   71.09148  120.55569  159.56063  229.73167
255.35290  300.74655
snipped
  [92] 3627.25753 3683.24696 3714.11421 3729.41203 3764.54192
3809.15159 3881.71016
  [99] 3917.16512 3932.00861

cumsum(rnorm(100, mean=40, sd=10))

   [1]   38.59288   53.82815  111.30052  156.58190  188.15454
207.90584  240.64078
snipped
  [92] 3776.25476 3821.90626 3876.64512 3921.16797 3958.83472
3992.33155 4045.96649
  [99] 4091.66277 4134.45867

The first realization did not make it in the expected 100 days so
further efforts should extend the simulation runs to maybe 120 days.
The second realization had him making it on the 98th day. There is an
R replicate() function available once you get a function running that
will return a specific value for an instance. This one might work:

min(which(cumsum(rnorm(120, mean=40, sd=10)) >= 4000) )

[1] 97

If you wanted a forum that does not explicitly discourage homework and
would be a better place to ask theory and probability questions, there
is CrossValidated:
http://stats.stackexchange.com/faq

Thanks in advance,
and apologies for the level of question...
Rainer

David Winsemius, MD
West Hartford, CT