Use of z-scores to find a normal probability
Although many programs (e.g. spreadsheets) can find normal probabilities directly for any normal distribution, it is instructive to find normal probabilities by first translating the problem into one involving a standard normal distribution (µ = 0, σ = 1). To do this, the end-points of the required interval are first transformed into z-scores.
Use the template at the top of the diagram to find z-scores corresponding to translate the question into one involving z-scores, then drag the vertical red lines to find the required area under the standard normal curve.
For a more accurate answer, type the end-points of the interval into the text-edit boxes above the diagram.
Repeat with at least five different questions until you have mastered the method.
Normal tables
The use of z-scores are essential if there is no computer to evaluate normal probabilities. Printed tables for the standard normal distribution can be used to look up the area to the left of any z-score.
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. (Note however that the lower template is not always needed.)
Again, repeat until you have mastered the method.