Probability Norm Exercises

Exercises

Worked solutions to these exercises can be found here: Q1

1. [math][L1,L2][/math] If [math]X\sim N(0,1)[/math] evaluate

   1. [math]\Pr (X\leq 0.23)[/math] {Solution: 0.5910}

   2. [math]\Pr (X\geq 0.23)[/math] {0.4090}

   3. [math]\Pr (-0.5 \leq X \leq 1.84)[/math] {0.6586}

2. [math]L1,L2[/math] Find the number [math]z_{0}[/math] such that if [math]Z\sim N(0,1)[/math]

   1. [math]\Pr (Z\geq z_{0})=0.05[/math] {1.645}

   2. [math]\Pr (Z\lt -z_{0})=0.025[/math] {1.96}

   3. [math]\Pr (-z_{0}\lt Z\leq z_{0})=0.95[/math] {1.96}

   and check your answers using EXCEL.

3. [math]L1,L2[/math] If [math]X\sim N(4,0.16)[/math] evaluate

   1. [math]\Pr (X\geq 4.2)[/math] {0.3085}

   2. [math]\Pr (3.9\lt X\leq 4.3)[/math] {0.3721}

   3. [math]\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right)[/math] {0.6170}

   and check your answers using EXCEL. (Note for part (c), define the “events” [math]A=\left( X\leq 3.8\right) [/math] and [math]B=\left( X\geq 4.2\right) [/math] and calculate [math]\Pr \left( A\cup B\right)[/math].