# Normal distribution Problem

• Oct 27th 2010, 03:05 AM
mastermin346
Normal distribution Problem
The height of students in a college is normally distibuted with mean,$\displaystyle \mu$ cm and standart deviation of 12 cm.Given the percentage of students with the height of less than 150 cm is 25%.Find the value of $\displaystyle \mu$

i get:

$\displaystyle z = \frac{X - \mu}{\sigma}$

$\displaystyle 0.25 = \frac{150 - \mu}{12}$

$\displaystyle \mu = 147$

• Oct 27th 2010, 04:36 AM
mr fantastic
Quote:

Originally Posted by mastermin346
The height of students in a college is normally distibuted with mean,$\displaystyle \mu$ cm and standart deviation of 12 cm.Given the percentage of students with the height of less than 150 cm is 25%.Find the value of $\displaystyle \mu$

i get:

$\displaystyle z = \frac{X - \mu}{\sigma}$

$\displaystyle 0.25 = \frac{150 - \mu}{12}$

$\displaystyle \mu = 147$

0.25 is a probabilty, not the value of z. More specifically, $\displaystyle \Pr(Z < z*) = 0.25$. So $\displaystyle z* = \frac{150 - \mu}{12}$. Your job is to get the value of z* using your tables, substitute it and then solve for $\displaystyle \mu$.