Difference between revisions of "Probability Norm Exercises"
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| − | <li><p>Find the number <math>z_{0}</math> such that if <math>Z\sim N(0,1)</math></p> | + | <li><p> (L1, L2) Find the number <math>z_{0}</math> such that if <math>Z\sim N(0,1)</math></p> |
<ol> | <ol> | ||
<li><p><math>\Pr (Z\geq z_{0})=0.05</math></p></li> | <li><p><math>\Pr (Z\geq z_{0})=0.05</math></p></li> | ||
Revision as of 12:07, 4 September 2014
(L1, L2) Find the number [math]z_{0}[/math] such that if [math]Z\sim N(0,1)[/math]
[math]\Pr (Z\geq z_{0})=0.05[/math]
[math]\Pr (Z\lt -z_{0})=0.025[/math]
[math]\Pr (-z_{0}\lt Z\leq z_{0})=0.95[/math]
and check your answers using EXCEL.
If [math]X\sim N(4,0.16)[/math] evaluate
[math]\Pr (X\geq 4.2)[/math]
[math]\Pr (3.9\lt X\leq 4.3)[/math]
[math]\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right) [/math]
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].
