In a contest of 100 students, marks are normal with mean 64 and standard deviation 16. How many scored between 30% and 70% inclusive?

1. Standardise with $z=\dfrac{x-\mu}{\sigma}$, taking $\mu=64$ and $\sigma=16$. 2. Lower limit: $z=\dfrac{30-64}{16}=-2.125$. Upper limit: $z=\dfrac{70-64}{16}=0.375$. 3. From tables $P(-2.125\le Z\le 0.375)=0.62938$. 4. Multiply by the 100 students: $0.62938\times 100\approx 63$. 5. The value $79$ comes from treating $0.3$ and $0.7$ as probabilities and applying the addition rule for non-mutually-exclusive events. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 1: Probability_