• Apr 29th 2009, 08:03 AM
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?
• Apr 29th 2009, 07:16 PM
mr fantastic
Quote:

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 $\displaystyle a$ and $\displaystyle b$ such that $\displaystyle \Pr(Z > a) = 0.25$ and $\displaystyle \Pr(Z < b) = 0.25$.

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

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

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

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