User:Kevin Tan/Probability Distribution

Example : If N(42, 9) , evaluate

(i) P(X < 44)

(ii)P(40 < X < 45)

Solution: To use the standardised normal distribution table, you’ve to understand :

1. that 42 is the mean and 9 is the variance.

       2.	Then, need to convert P(X)  to P(Z)   by using the
               formula P(Z < [math]\frac{x-\mu}{\sigma})[/math]

3.

Std Normal Distribution

       4.  The area below the curve is the probability, corresponding to the value of ‘z’ and         the value from the table is just for the shaded region.
       5.  The graph is a symmetrical graph and we are reading the area of HALF the graph only.
       6.  The total area under the graph is 1 (ONE) and area of 0.5 on each side.

The worked example below will hopefully make it clear,…..