A random variable $X$ has a binomial distribution with $n=6$ and probability of success $p$. Given t

Question

A random variable $X$ has a binomial distribution with $n=6$ and probability of success $p$. Given that $\mathrm{P}(X[2] Given that $\mathrm{P}(X=3)=0.08192$, show that $p$ satisfies the equation $p(1-p)=k$, where $k$ is a constant to be determined. Given further that $p[4] It is now given that $p=\frac{1}{4}$. Find $\mathrm{P}(X=4)$, giving your answer as a fraction. [1] The mean and standard deviation of $X$ are denoted by $\mu $ and $\sigma $ respectively. Find $\mathrm{P}(\mu -\sigma [5]

Accepted Answer

(i) $p = 0.703$ (ii) $k = \frac{4}{25}$, $p = \frac{1}{5}$ (iii) $\frac{135}{4096}$ (iv) $0.65$

2007 H1 Q9 [Modified]

2007 H1 Q9 [Modified]

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