A magazine has a set limit of 3000 on the word count of its articles. The editor has noticed that the articles sent for publication are consistently over the limit and she estimated that the distribution of the word counts is $$N(3500, \sigma^2)$$.
a) Find $$\sigma^2$$ if only 20% of the submitted articles meet the word limit of 3000.
b) Determine what the word limit should be if we want 90% of the submitted articles to meet it.
c) What is the proportion of submitted articles with word counts between 3100 and 3300?
Any help or hints would be appreciated! Thanks!