Problem
2. A discrete random variable $X$ is modelled by the binomial distribution. Khunsha uses tne binomial cumulative probability feature of her calculator to find $\mathrm{P}(X \leq 4)$ and $\mathrm{P}(X \leq 8)$. Which one of the following is the same as $\mathrm{P}(X \leq 8)-\mathrm{P}(X \leq 4)$ ? \[ \mathrm{P}(4 \leq X \leq 8), \quad \mathrm{P}(4 \leq X \leq 7), \quad \mathrm{P}(5 \leq X \leq 8), \quad \mathrm{P}(5 \leq X \leq 7) \] Explain your answer.
Solution
Step 1 ：\(\mathrm{P}(X \leq 8) - \mathrm{P}(X \leq 4) = \mathrm{P}(5 \leq X \leq 8)\)
Step 2 ：\boxed{\mathrm{P}(5 \leq X \leq 8)}
