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I think we are using the same rules, just different z-tables (with different levels of precision). So at the end of the day, I think you were right on both questions, and the person who wrote the answer was probably just using a different z-table.

I think you were close to being correct for part a), it's just that it looks like you used the 95% approximation, rather than using the exact rule. In other words, rather than P(X>120) = (1-0.95)/2 = 0.025, you should instead use the more precise: P(X>120) = (1-0.9545)/2 = 0.02275 Part b) it...

Yes, that is the precisely correct answer. The 95% between 2 standard deviations of the mean is just an approximation after all (it is exactly 95.45%). The exact answer for part b) should be P(90 < X < 120) = P(X<120) - P(X<90) = 0.9772 - 0.1587 = 0.8185 (which is quite close to what you got).

Very interesting. What did they have as the answer for part a)?

I think 2.5% makes sense for part a), since the standard deviation is 10, and for a normal distribution 95% of values fall within two standard deviations from the mean (so that would be 2.5% above 120 and 2.5% below 80). Was both your part a) and part b) marked as wrong? Or just part b)?

Nah I only have this one question. A student submitted it to me for help through my website www.tickboom.study. I asked them where it came from because at first I was convinced it couldn't have been a high school question.

Yes I was thinking squeeze theorem might help too. Especially given part iv) involved finding a lower and upper bound. But I can't work out how to get those bounds as a function of n, in order to then work out their limit as n goes to infinity ... But I suspect there may be some way to do it by...

It's taken from a bespoke exam written at Baulkham Hills. Apparently a concoction of difficult questions to help prepare for the hardest possible things that might pop up on the final exam. I'm thankful I didn't get a question like this when I sat the HSC!

Yeah when I first saw it I also thought it was a Uni question. But so far I've only needed high school concepts. Part i) requires induction. Parts ii), iii) and iv) require you to compare the shaded area under the curve (i.e. the integral) with the shaded area under rectangles. Part v) I just...

I thought the same thing when I saw it! But the person who shared it with me confirmed it was on a (very hard) 4U math exam.

Does anybody have any ideas on how to approach part v) of this question? I've managed to do parts i), ii), iii) and iv), but v) is eluding me!

If you are struggling with a math question and need some help, try heading to my website: tickboom.study You simply share a photo of the question you a struggling with, I record a video of me working out the solution, and then send you a link to the video. It is 100% free and easy to use, so...

Pedro, I don't think you get to pick any unique integers for a, b, c and d. I think the question is just stating that the solution to the equation is (a+b+c+d)/4 where a, b, c and d (whatever they happen to be) are unique and integers. Check out this video to see my attempt at tackling the...

Check out the following video if you would like a step-by-step solution:

You may find this video explanation helpful, where I show a few alternative ways to think about this one. Enjoy!

You may find this video helpful, where I work through a detailed explanation of one possible approach: Enjoy!