Calculating probabilities with normal distributions directly is extremely difficult (the formula is . What's worse is that every unique situation (weights of dogs, height of grass, lifespan of light bulbs, grades in statistics, etc.) would require a unique set of calculations.

So in order to save everybody some time, the probability calculations for a normal distribution with a mean of 0 and a standard deviation of 1 have been calculated and are readily available in tables (there's probably one in the back of your textbook). All we have to do is to convert the information from our normal distribution to the standard normal distribution. Here's the formula:

The represents the particular data point from your population. The represents the mean of the population, and the represents the standard deviation. The is the converted data value for the standard normal distribution.

Since this question starts with a data point (mothers younger than 24.5) and asks for a percentage, we will begin by calculating the z-score of our data point:

Now we need to go find a table of z-scores and look up the percentage that is associated with a z-score of -1.8. The table that I used listed the value as .0359 or 3.59%. To one significant digit, the percentage would be 4.0%

This method will work for any data point you need to test, as long as the data in question is normally distributed.