# How to estimate the standard deviation in this normal distribution?

There is this simple looking basic statistics question that asks to estimate its mean and standard deviation. I have some doubts and just want to make sure whether my working is correct.

For part (i) Is it ok if I say the estimated mean is 41? I think this one is pretty straightforward.

For part (ii) it is very tempting to say the s.d. is 2, but between the 1st quartile and 3rd quartile we have 50% of the data, while for a normal distribution about 2/3 (not 50%) of the data lie between 1 s.d from the mean. Thats the only clue that I can think of. Is there any other way to estimate the s.d.?

Helps are greatly appreciated. Many thanks!

As for the standard deviation, you can find for example here: http://en.wikipedia.org/wiki/Box_plot#mediaviewer/File:Boxplot_vs_PDF.svg that approximately 50% from your data lies between 0.6745 standard deviations from the mean. So I would say a good estimate of your standard deviation is $\frac{12}{0.6745} \approx 17.79$.