A Normal distribution is described by a Normal density curve Any particular Normal distribution is completely specified by two numbers: its mean ???? and its standard deviation ???? The mean of a Normal distribution is the center of the symmetric Normal curve The standard deviation is the distance from the center to the change-
have a normal distribution • The normal distribution is easy to work with mathematically In many practical cases, the methods developed using normal theory work quite well even when the distribution is not normal • There is a very strong connection between the size of a sample N and the extent to which a sampling distribution approaches
calculated over intervals rather than for speci c values of the random variable Although many types of probability density functions commonly occur, we will restrict our attention to random variables with Normal Distributions and the probabilities will correspond to areas under a Normal Curve (or normal density function)
Normal Distributions37 from the menu to standardize By selecting “Subtract mean and divide by standard deviation” the command calculated the standardized values, z=(x?x)s The results can be stored in C2 The standardized vocabulary scores (or z?score) will tell how far above or below the mean a particular score falls
Perhaps the most important ideal distribution used is the 'normal' distribution (Figure 6 1) Once one understands the characteristics of the normal distribution, knowledge of other distributions is easily obtained Figure 6 1 The normal distribution Most people are familiar with the normal distribution described as a “bell-shaped curve,”
Normal Distributions Probabilities correspond to areas under the curve and are calculated over intervals rather than for specific values of the random variable
One of these assumptions is that the sampling distribution of the mean is normal That is, if you took a sample, calculated its mean, and wrote this down; then