IB Mathematics Applications & Interpretation Question Type 2: Finding the P-value or Critical Value Given the Other for a Specific Distribution Exercises

For $X\sim N(5,9)$, calculate the p-value for observing $X\ge 11$.

For $X\sim N(5,9)$, calculate the p-value for observing $X>8$.

For $X\sim N(5,9)$, find the value $a$ such that $P(X>a)=0.07$.

For $X\sim N(5,9)$, find $c>0$ such that $P(|X-5|>c)=0.07$.

For $X\sim N(5,9)$, calculate the $p$-value for observing $X<2$.

For $X\sim N(5,9)$, find the critical value $c$ such that $P(X\ge c)=0.01$.

For $X\sim N(5,9)$, find $c>0$ such that $P(|X-5|<c)=0.93$.

For $X\sim N(5,9)$, find the critical value $a$ such that $P(X<a)=0.07$.

For $X\sim N(5,9)$, find the critical value $c$ such that $P(X\le c)=0.025$.

For $X\sim N(5,9)$, given an observed value $x_0=10$, calculate the two-sided $p$-value for testing $H_0:\mu =5$.

For $X\sim N(5,9)$, calculate the $p$-value for observing $X\le -1$.

Given that $X\sim N(5,9)$, calculate $P(2\le X\le 8)$.