Using the formula : $p = 1 - k^{-2}$
I calculated that $p = 1 - 1.5^{-2} = 0.56$ , which equals to $56\%$.
Because I have $24$ data points I go ahead and solve the number of points is $56\%$ of $24$:
\begin{equation} \frac{56 * 24}{100} = 13.44 \end{equation}
which is approximately 13, which was my final answer.
For some reason this is not the final answer therefore my answer 13 is wrong.
What did I do wrong?
On
By Chebyshev's inequality,
$P(|X-\mu|\geq k \sigma) \leq \frac{1}{k^2}$
$\implies P(|X-\mu|<k\sigma)>1-\frac{1}{k^2}$
For $k=\frac{3}{2}$, we have R.H.S. bound as $\frac{5}{9} \approx 0.5555556$, so that number of data points $=24 \times \frac{5}{9}\approx 13$
By Chernoff's inequality, we can get stronger tail bounds:
$P(X\geq \mu +k\sigma) \leq e^{-k^2\sigma^2/3\mu}$ and
$P(X\leq \mu - k\sigma) \leq e^{-k^2\sigma^2/3\mu}$
$\implies P(|X-\mu| <k\sigma) > 1-2e^{-k^2\sigma^2/3\mu}$
When you calculate the p do not round up, instead it'll just be (55%*24)/100=13.33 which is the correct answer.