# [R] Normal Distribution Quantiles

Bert Gunter gunter.berton at gene.com
Sat Jan 8 22:48:21 CET 2011

If I understand what you have said below, it looks like you do NOT
have the problem solved manually. You CAN use qnorm , and when you do
so, your equation yields a simple quadratic which, of course, has an
exact solution that you can calculate in R.

Of course, one can use uniroot or whatever to solve the quadratic; or
simulation or interpolation using pnorm. But other than the R
practice, these are unnecessary and, in this case, a bit silly.

Cheers,
Bert

On Sat, Jan 8, 2011 at 6:25 AM, Rainer Schuermann
<Rainer.Schuermann at gmx.net> wrote:
>> 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
>>
>> >
>> > and apologies for the level of question...
>> > Rainer
>> >
>> > ______________________________________________
>> > R-help at r-project.org mailing list
>> > https://stat.ethz.ch/mailman/listinfo/r-help
>> > and provide commented, minimal, self-contained, reproducible code.
>>
>> David Winsemius, MD
>> West Hartford, CT
>>
>>
>
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