# [R] Normal Distribution Quantiles

Michael Bedward michael.bedward at gmail.com
Mon Jan 10 03:36:56 CET 2011

Just to add to the silly solutions, here's how I would have done it...

mu <- 40
sdev <- 10
days <- 100:120 # range to explore
p <- 0.8
days[ match(TRUE, qnorm(0.2, mu*days, sqrt(sdev * sdev * days)) >= 4000) ]

Michael

On 9 January 2011 08:48, Bert Gunter <gunter.berton at gene.com> wrote:
> 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
>>>
>>> >
>>> > Thanks in advance,
>>> > and apologies for the level of question...
>>> > Rainer
>>> >
>>> > ______________________________________________
>>> > R-help at r-project.org mailing list
>>> > https://stat.ethz.ch/mailman/listinfo/r-help
>>> > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>> > and provide commented, minimal, self-contained, reproducible code.
>>>
>>> David Winsemius, MD
>>> West Hartford, CT
>>>
>>>
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
>
> --
> Bert Gunter
> Genentech Nonclinical Biostatistics
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>