Inverse problem

In the earlier exercises, you were given a range of x-values and were asked for the probability of getting a value in this range. The inverse problem gives you a normal probability and asks for the corresponding values of X.

 

In the exercises below, decide whether the question specifies the area to the right or left of x. Then drag the vertical red line to find x giving approximately the correct area.

A more accurate answer can be found with 'trial and error' by typing adjacent values in the text-edit box above the normal curve.

Repeat with different questions until you have mastered the method.

Using normal tables

This type of question can also be answered using normal tables. Firstly find the range of z-scores that gives the required probability, then transform this interval into the actual measurements with:

x  =  μ  +  z σ

 

The next exercise is similar to the one above, but a standard normal table should be used to find areas under the normal curve.

Since the table only gives the area to the left of any z-score, you may need to subtract such areas to answer the question. A template is provided for this purpose.

Again, repeat until you have mastered the method.