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In a contest of 100 students, marks are normal with mean 64 and standard deviation 16. How many scored between 30% and 70% inclusive?
A79
B63
C74
D50
Answer & Solution
Correct answer: B. 63
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_
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