# [SOLVED] Normal Distrubtion Question

• Apr 15th 2008, 11:21 PM
looi76
[SOLVED] Normal Distrubtion Question
Question:
Given that $X \sim N(44,25)$, find $t$ correct to 2 decimal places when
$P(X \geq t)=0.7704$

Attempt:

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

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

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

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

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

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

$1.3 = X - 44$

$X = 45.3$

Where did I go wrong?
• Apr 16th 2008, 01:57 AM
jjzshen
Quote:

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

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

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

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

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