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?
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 $\displaystyle n$.