1. ## 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?

2. 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 $\displaystyle p ( V < 230)= ?$

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

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

ii) = $\displaystyle P(230<V<260)$

iii) $\displaystyle p(V>230)$