Is writing ability associated with IQ or intelligence? Is greater ability to write well i.e. analysis of books/literature/research papers associated with higher I.Q. scores? 
Statistically speaking, is writing ability normally distributed like I.Q. is?
The second question (normality) is somewhat easier to answer because it depends less on the exact measures used.


  reading and writing abilities are normally distributed in the general education framework.


Meaning for people who are actually schooled and tested (in the US for the above study). The sample for the above was "316 boys and girls who were assessed annually in grades 1 through 4".

As for the first question (association between IQ and writing ability), the qualitative answer is obviously going to be yes. There is even one proposal to use samples of written text to estimate the writer's IQ!


  The primary focus of this research is to introduce a
  method of measuring an individual’s IQ by analyzing
  the vocabulary in said individual’s writing. In this
  paper, we show that the ratio of SAT words in a
  dataset of writing samples is roughly normally
  distributed, though with an obvious left skew. We go
  on to show a method that can be used to calculate an
  individual’s IQ with this ratio and provide samples
  with measured accuracy. 


Alas, the claim isn't terribly well supported because the IQ was self-reported for the sample they used to test their assumption.

Found a study relating to 2nd laguage acquisition:


  The result of this study revealed that IQ made significant contribution in predicting reading comprehension (23.42%) and writing achievement (16.08%). 


I don't have the full text, and the abstract isn't terribly clear, but presumably the amount of langauge education was standardized somehow... otherwise this result makes little sense.

From a more elaborate study (primary language) there are various intermediate factors affecting the various measures of writing quality... but most of these intermediate factors correlated with non-verbal IQ as well:




  As shown in Table 3, there were moderate correlations between the scores on the
  cognitive background tests, except for the measure of attention in dichotic listening
  which did not correlate significantly with any of the other variables. [...]
  
  While the narrative product measures were significantly correlated with a number of
  cognitive abilities, the narrative process measures were only correlated with reading
  and spelling skills (see Table 6). Children with better reading and spelling abilities
  made more online revisions than their peers. Moreover, children who were good
  spellers transcribed faster than their peers. The cognitive measure of selective
  attention was significantly associated with the ability to use capitalization and
  punctuation in writing.
  
  [...] Although narrative macrostructural quality was correlated with a number of cognitive measures, only oral language skills and spelling were significant
  predictors in the final model, implying that the other measures did not significantly add to the model’s prediction.