For example, look at Q1(a) from the 2018 Probability paper:
(a) Over the last seven years, the daily temperatures in Reefton have been found to be approximately normally distributed with a mean of 11.6°C and standard deviation of 4.8°C.
Use this approximation to answer the questions in parts (i) to (iv).
Working and/or diagrams must be shown. Correct answer(s) alone will generally limit grades to Achievement.
*(i) Find the probability that a randomly chosen day in Reefton would have a daily *
temperature between 11.6°C and 18.8°C
(ii) Find the probability that a randomly chosen day in Reefton would have a daily temperature over 17°C.
(iii) People in Reefton talk about the hottest 1% of days as being “scorchers”.
What is the lowest possible daily temperature of a “scorcher” day?
(iv) Using this normal distribution approximation, the probability of a daily temperature lower than 9°C is 29.4% (3sf).
Suppose that temperatures in Reefton increased due to climate change, but the standard deviation remained the same.
What would the mean daily temperature for Reefton need to become to make this probability fall to 20.0% (3sf)
If you spend a minute briefly looking at the questions, you will notice that (i) and (ii) are one step problems which won’t give you more than a “u” (leading to an Achieved grade). On the other hand, (iii) requires you to calculate Z value and find a value when you know probability. This is a two-step solution and it would usually give you an “r”, which will give you 5 marks (M5) on the question even if you haven’t done the previous two sub-questions. That is because by completing (iii) you would demonstrate the skills required to complete (i) and (ii).
Even a quick look on (iv) tells us that it is a solution in several steps so we would expect an “r” or even “t” for it. Remember, a single “t” mark in one question gives you 7 marks (E7) which is a third of your final Excellence.
So to keep it on the safe side, you could only complete (iii) and (iv), and (iii) would be just in case you made a mistake in (iv) so you would at least get an “r”.
After that you can move on to the next part. If you have completed the Merit/Excellence questions for all 3 questions, and still have time left, you could go back and do the Achieved parts.