\[X\]
follows a normal distribution with mean \[\mu\]
and standard variance \[\sigma^2\]
.We write
\[X \sim N( \mu , \sigma^2)\]
.Just knowing that a random variable follows a normal distribution is not a lot of use if we cannot calculate the probability of
\[X\]
taking a certain value, or given a probability, finding the correspomnding value of \[X\]
.To be able to do this we use the Z - transform to transform any normal distribution
\[N( \mu , \sigma^2 ) \]
onto the standard normal distribution \[N(0, 1)\]
.The Z - transform is
\[Z=\frac{X - \mu}{\sigma}\]
. Using the transform means we can use a single table instead of a range of tables for possible values of \[\mu\]
and \[\sigma\]
.