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 $X>8$.

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

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 $a$ such that $P(X>a)=0.07$.

For $X\sim N(5,9)$, calculate the p-value for observing $X\ge11$.

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

For $X\sim N(5,9)$, calculate the p-value for $2\le X\le8$.

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

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 $x_0=10$, compute the two-sided p-value for testing $\mu=5$.

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 $P\bigl(|X-5|>c\bigr)=0.07$.