- 1). Find the average or mean of your data set. You can calculate this yourself by adding all the values and dividing that sum by the quantity of values in your set. You can also use the "μ" (mu) key on a statistical or scientific calculator. For example, perhaps you measured the heights of all students in a school and found the average height to be 42 inches.
- 2). Find the standard deviation of your data set. This is a statistical parameter that represents the amount of variation or spread in your data. This is time-consuming to calculate by hand, but you can use the "σ" (sigma) key on your calculator to find this value. In the case of the example, you find the standard deviation of heights to be 2.5 inches.
- 3). Determine the value (x) for which you want to calculate probability. Suppose you're designing a play structure and want to ensure enough overhead clearance for students walking beneath it. You wish to determine the probability that a student picked at random will be taller than 48 inches.
- 4). Translate your chosen value into a Z score. To calculate the Z score, use the following equation: z = (x - μ)/σ. The calculation in the case of the example would be z = (48 - 42)/2.5 = 2.40.
- 5). Look up the probability value associated with your Z score on a standard table of Z values. To do so, find the first two digits of your Z score along the leftmost column of the table, which gives you the row you need. Then find the third digit of your Z score on the uppermost row of the table; this gives you the column you need. Where your row and column meet, you will find the probability value associated with your Z score. For the example above, the associated probability is 0.4918.
- 6). Subtract the probability you just determined from 0.5. This gives you the probability of finding a number in the data set that is greater than your value. The reason for this step is that the Z table actually gives the probability of finding a value between the average and your Z score. The probability in the case of the example would be calculated as 0.5 - 0.4918 = 0.0082.
- 7). Multiply the result of your last calculation by 100 to change it into percentage form. You now have the probability that a randomly chosen number in your normally distributed data set will exceed the value you chose. For the example, the probability that a student you choose at random has a height exceeding 48 inches is 0.82 percent.
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