germany-abitur 2022 QB 1d

germany-abitur · Other · abitur__bayern_stochastik 3 marks Normal Distribution Multiple-Choice Conceptual Question on Normal Distribution Properties
In general, the following inequality holds for a random variable $X$ with expected value $\mu$ and standard deviation $\sigma$ for $k > 0$ :
$$P ( \mu - k \cdot \sigma < X < \mu + k \cdot \sigma ) \geq 1 - \frac { 1 } { k ^ { 2 } }$$
Explain the statement of this inequality for $k = 2$. 
In general, the following inequality holds for a random variable $X$ with expected value $\mu$ and standard deviation $\sigma$ for $k > 0$ :

$$P ( \mu - k \cdot \sigma < X < \mu + k \cdot \sigma ) \geq 1 - \frac { 1 } { k ^ { 2 } }$$

Explain the statement of this inequality for $k = 2$.
Paper Questions
QA a QA b QB 1a QB 1b QB 1c QB 1d QB 2a QB 2b