# Normal Distribution

• May 17th 2009, 08:09 AM
A Beautiful Mind
Normal Distribution
Suppose that a machine filling bottles of paediatric liquid paracetamol fills the bottles so that the mean volume of the bottles is 250ml with a standard deviations of 20ml.
If a bottle is selected at random what is the probability that:

i) the volume of the bottle will be less than 230ml;
ii) the volume of the bottle will be between 230ml and 260ml;
iii) more than 230ml?
• May 17th 2009, 08:41 AM
Tweety
Quote:

Originally Posted by A Beautiful Mind
Suppose that a machine filling bottles of paediatric liquid paracetamol fills the bottles so that the mean volume of the bottles is 250ml with a standard deviations of 20ml.
If a bottle is selected at random what is the probability that:

i) the volume of the bottle will be less than 230ml;
ii) the volume of the bottle will be between 230ml and 260ml;
iii) more than 230ml?

use the formula to standardize it, v = volume so $p ( V < 230)= ?$

$p(Z< \frac{230-250}{20} )= -1$= $p(Z<-1)$

$p(Z<-1) = 1-p(Z<1) = 1-0.8413= 0.1587$

ii) = $P(230

iii) $p(V>230)$