Okay, so this is from the 2008 HSC, and don't freak out because this question stumped me at first too!
Part ii) states, "Rachel is 10 1/2 years of age"; I'm not really sure why the image you linked to has that information missing, but hopefully it will help clarify things!
1) If 2.5% of girls of the same age are taller than Rachel, how tall is she?
So I hope that I'm not going to confuse you further, but what would be most helpful is to draw a simplified normal distribution diagram, like the one featured on this page:
http://rapidlearningcenter.com/mathematics/introductory-statistics/08-The-Normal-Distribution.html
If 2.5% of girls are taller than Rachel, then looking at the diagram, we can see that 2.5% is from where the pink line ends and the green line starts. (One standard deviation from the normal distribution is 68%, two standard deviations are 95% and three are 99.7%) So, this means that Rachel has a Z-score of 2. (I really hope this makes sense - it is kind of hard to explain in writing as it is kind of a visual thing)
Now, find 10 1/2 on the graph, and then go up until you reach the line marked 2. This points meet at 155cm, therefore Rachel is 155 cm.
2) Rachel does not grow any taller. At age 15 1/2, what percentage of girls of the same age will be taller than Rachel?
Again, draw a simplified normal distribution diagram. We can see form the graph provided that at age 15 1/2 and a height of 155cm gives a z-score of -1. Now, I'm not entirely sure if this is the 'proper' way to get the answer, but it worked for me and I got the answer right! Ok, the total diagram makes up 100%, so if you split the distribution graph in half (not literally!), all the z-scores from 0 up give 50%. Since -1 is on the lower half of the graph, we have to divide 68% by two in order to give the percentage for that single part of the graph - this gives 34%. Plus 50% and 34% together and you get 84% of girls being taller than Rachel.
Really hope that helped! All the best for general maths on Tuesday!
God Bless!
