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Solving Problems that Involve the Normal Distribution - Graphics require Java

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The following will calculate probabilites but has no graphics

Calculation of Probabilities Using the Normal Distribution

    If the problem involves one z value
  1. Calculates P(z < some value)
  2. and P(z > some value)
  3. Except for rounding errors values should add to 1.00
  4. If the problem involves two z values
  5. Calculate P(z < given value one)
  6. P(given value 1 < z < given value 2)
  7. P(z > given value 2)
  8. Except for rounding errors values should add to 1.00
Input z values can vary from -3 ro +3 and may have up to three digits after the decimal point. For example any of the following would be valid entries: 2., 2.5, 2.57 and 2.575 The model assumes that virtually all of the area under the curve lies between -3 and +3 standard deviations from the mean. For most applications this is a reasonable safe assumption. In checking this tool against the tables in statistics textbooks I found that this tool usually gives answers that are with a few ten-thousandths of the values given in the books. In general the further you are from the mean the better the agreement.



Standard Normal Probability Distribution Data Input
Input first z score
Input second z score if there is one
Ouput Probabilities
P(z < zcrit1)
P( zcrit1 < z < zcrit2)
P( z > zcrit2)
Comments and/or errors

Working with the normal probability distribution should be easy! It is a very well behaved distribution and the calculations are relatively simple. The hardest part usually involves reading the problem and reading the tables in the textbook. If all goes well this tool will help you understand what is going on and allow you to read and understand the tables like a pro. To use this tool you must have Java Installed. If you don't have Java and don't want it there is a companion tool that doesn't use graphics that you can use. Frankly I don't think it is as good as this one (and I wrote it) but it may do the trick for you.

The usual question in statistics involves determining the probability of something. For a continuous distribtion such as the Normal the area under the curve represents probability. Problems usually ask you to determine the probability that some value will be between two other values. Examples of questions are:

The figure on the right provides you with a graphical view of some questions that you could be asked. The table in your textbook starts from the left-tail and goes to the right-tail. As it goes it gives you the cumulative probability to the current point. The point is defined by a z value. Virtually all of the area under the curve will be between z = -3 and z = +3. In otherwords from 3 standard deviations below the mean to 3 standard deviations above the mean. The tables can sometimes be confusing. A picture usually helps. Here is what the tool will do for you: