# [SOLVED] Normal Distrubtion Question

• Apr 15th 2008, 10:21 PM
looi76
[SOLVED] Normal Distrubtion Question
Question:
Given that $\displaystyle X \sim N(44,25)$, find $\displaystyle t$ correct to 2 decimal places when
$\displaystyle P(X \geq t)=0.7704$

Attempt:

$\displaystyle = P(X \geq t)=0.7704$

$\displaystyle \mu = 44$ , $\displaystyle \sigma^2 = 25$, $\displaystyle \sigma= 5$

$\displaystyle = P(\frac{X-\mu }{ \sigma } \geq \frac{X-44}{ 5})$

$\displaystyle 1 - \frac{X-44}{5} = 0.7704$

$\displaystyle 1 - 0.7704 = \frac{X-44}{5}$

$\displaystyle 0.26 = \frac{X-44}{5}$

$\displaystyle 1.3 = X - 44$

$\displaystyle X = 45.3$

Where did I go wrong?
• Apr 16th 2008, 12:57 AM
jjzshen
Quote:

Originally Posted by looi76
Question:
Given that $\displaystyle X \sim N(44,25)$, find $\displaystyle s$,$\displaystyle t$,$\displaystyle u$, and $\displaystyle v$ correct to 2 decimal places when
$\displaystyle P(X \geq t)=0.7704$

Attempt:
$\displaystyle = P(\frac{X-\mu }{ \sigma } \geq \frac{X-44}{ 5})$

$\displaystyle 1 - \frac{X-44}{5} = 0.7704$

This is the problem here. You need to use a normal probability table to find that
$\displaystyle \Pr(Z \geq -0.74) = 0.7704$

Then we have:
$\displaystyle -0.74 = \frac{t-44}{5} \Rightarrow t = 40.3$