2022 CJC P2 Q10
The random variable $X$ has distribution $\text{B}\left( n,p \right)$. It is given that the mean of $X$ is $4.5$ and the variance of $X$ is $3.15$.
(i)
Find the values of $n$ and $p$.
[3]
(ii)
Using the values of $n$ and $p$ found in part (i), find $\text{P}\left( X\ge 5 \right)$.
[2]
Do not use a calculator in answering this part.
It is given instead that the mode of $X$ is $10$ and $p=\frac{1}{2}$.
(iii)
By considering $\text{P}\left( X=10 \right)>\text{P}\left( X=9 \right)$ and $\text{P}\left( X=10 \right)>\text{P}\left( X=11 \right)$, write down an inequality involving $n$ and find the value of $n$.
[4]
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