Normal distributions are a family of distributions that have the same general shape. They are symmetric with scores more concentrated in the middle than in the tails. Normal distributions are sometimes described as bell shaped. Examples of normal distributions are shown to the right. Notice that they differ in how spread out they are. The area under each curve is the same. The height of a normal distribution can be specified mathematically in terms of two parameters: the mean (m) and the standard deviation (s).
<br>The height (ordinate) of a normal curve is defined as:
<br>where m is the mean and s is the standard deviation, p is the constant 3.14159, and e is the base of natural logarithms and is equal to 2.718282.
<br>x can take on any value from -infinity to +infinity.
<br>The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Normal distributions can be transformed to standard normal distributions by the formula: z=(x-m)/s
<br>where X is a score from the original normal distribution, m is the mean of the original normal distribution, and s is the standard deviation of original normal distribution. The standard normal distribution is sometimes called the z distribution. A z score always reflects the number of standard deviations above or below the mean a particular score is. For instance, if a person scored a 70 on a test with a ...
The solution is an overview of how the probability process works.