Worried about criteria D & E for IA on Normal Distribution

[studying]

So I'm currently writing my math IA and it involves me proving whether or not a set of sample data I found is normally distributed. For the method, what I did was:

• Find the mean, median, and mode (if they're all the same the data is normally distributed)
• Find the percentage of data that lies within a certain standard deviation from the mean (i.e 68.3% should lie between (mean - standard dev.) and (mean + standard dev.))
• Use the Pearson's goodness of fit test (aka chi squared test)

I'm in math SL so what the rubric says for criteria E (use of mathematics, out of 6) is that the IA shouldn't involve a lot of "prior learning". However finding the mean, median, and mode are all prior learning and really easy- same with the second bullet point ^, all I'm doing is substituting values into my calculator... Should I try to make my IA more complicated? If so does anyone have any suggestions on how??

I'm also worried about criteria D (reflection, out of 3) cause I don't feel like there's much you can do on that with normal distributions. Does anyone know how rigorous or sophisticated IB wants your critical analysis to be? Cause at this point I have no idea how I can bring more of that into my IA when all I'm talking about is statistics and normal distribution. 

Thanks in advance!! 

[IB Math Helper]

Mean, median and mode are part of the current curriculum. They are also part of the prior learning but I wouldn't worry about that since it is also part of the SL curriculum (I think some countries teach mean, median and mode in lower grades while others do not). 

Your topic should be more sophisticated than just determining whether a distribution is normal or not. The normal distribution properties are desirable because mathematicians understand it very well. But what if a distribution is not normal? What happens then? If you can look into what can be done to transform a distribution to a normal distribution, that would be helpful. If you can't, state what one can/should do. Thinking about these questions should help your IA.