Calculate the mean average of your data. You can do this manually with a calculator or with pencil and paper by adding together each value, and then dividing by the total number of values. Alternately, you may use the average function in a program like Excel, or a programmable calculator. If you are given the mean average in the question, skip this step.
Calculate the standard deviation of your data. You can do this manually by first making a table with your original data in one column, and the mean value, clearly labeled, in the bottom row of that column. In the next column, calculate the deviation of every value of your data, by taking the absolute value of the difference between the mean value and each individual value. Finally, take the mean average of all these deviations by adding them together and dividing by the number of values, and record this as your standard deviation. If you are given the standard deviation in the question, skip this step.
Sketch a graph of the normal distribution, and label the following points. On the x-axis, label the center of the curve with your calculated mean value, and divide the curve with an axis of symmetry at this point. The question will ask you the percentage or fraction of the population that will be greater than or less than a particular value, or between two values. Mark the value or values on the graph. If the values are not raw but given in terms of standard deviations, do not label the graph with them yet.
Determine the standardized normal distribution from your normal distribution. Given your point or points, rewrite them in terms of the number of standard deviations from the mean value, or z-score. Subtract each value from the mean of your data, then divide by the standard deviation of your data. Round off to the same number of decimal places available on your table of standard normal distribution. (The most common number is two.) Draw a new normal distribution graph with these values. The standardized value of your mean should be zero on the standardized graph, and your y-axis should pass through this point. If you were already given a value or values in standardized form, place them on the graph now.
Shade in the area under the curve corresponding the range of x-values given in the question.
Determine the area under the curve that is shaded. This corresponds to the fraction of the population falling within the given range of values. The table of standard normal distribution will tell you the area under the curve between x=0 and the value you are looking for. Determine the area corresponding the x-value or values given, then mark off and label that area of the graph with that value. In the case of a negative x-value, drop the negative when looking up the area, but make sure to label the area on the left side of the curve.
Use the labeled areas under the curve to determine the area of the shaded part of the curve. If you are looking for probability of an x-value between zero and a positive or negative number, your shaded area will already by labeled. If you are looking for the probability between two positive x-values, the shaded area will come from subtracting the area from x=0 to the smaller x-value from the area between x=0 and the larger x-value. (The area between two negative x-values is the same.) For the probability of values above a certain positive x-value (or below a certain negative x-value), subtract the labeled area from the area of the entire right (or left) side of the curve, which has a value of 0.5. In the case of the probability of values between a negative and positive x-value, add the two labeled areas together.
Write your final answer. The form is, "The probability of a value between A and B is approximately (area) for the given population." To convert the probability from decimal form to percentage form, multiply by 100.