# Math Help - Normal distribution, help please

1. ## Normal distribution, help please

OK I have a normal distribution N(m,v) (mean and variance unknown) I have been given the values of the lower and upper quartiles of this distribution, they are 2/3 and 4. How do I find the mean and variance with just this information?

2. Originally Posted by Jeff1987
OK I have a normal distribution N(m,v) (mean and variance unknown) I have been given the values of the lower and upper quartiles of this distribution, they are 2/3 and 4. How do I find the mean and variance with just this information?
Use tables or technology to find the value of $a$ and $b$ such that $\Pr(Z > a) = 0.25$ and $\Pr(Z < b) = 0.25$.

From $Z = \frac{X - \mu}{\sigma}$:

$a = \frac{4 - m}{\sigma}$ .... (1)

$b = \frac{\frac{2}{3} - m}{\sigma}$ .... (2)

Solve equations (1) and (2) simultaneously for $m$ and $n$.