The random variable $X$ has distribution $N(\mu, \sigma^2)$. Given that \(P(X k) = 0.4

Question

The random variable $X$ has distribution $N(\mu, \sigma^2)$. Given that $P(X > k) = 0.45$, find the value of $P(X > 2\mu - k)$.[2] It is given that $\mu = 4$ and $P(1 < X < 4) = 0.2475$. Find the value of $\sigma$.[2] Draw a sketch to show the distribution of $X$ for $x$ between $-11$ and $19$.[2]

Accepted Answer

(a) $0.55$ (b) $\sigma=4.50$ (c) Normal curve centred at $x=4$ over $-11\le x\le19$

2025 VJC P2 Q9

2025 VJC P2 Q9

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