standard scores with same mean µ = 0 and standard deviation ? = 1 (i e under the same standard condition) so that we can tell who got a better mark (The standard normal distribution is a normal probability distribution with µ = 0 and ? = 1, and the total area under its density curve is equal to 1 ) We use the formula ????= ???? to convert
common practice is to convert everything to a standard normal distribution and use the same normal distribution table over and over The z-score formula for converting a normal random variable X into the standardized normal random variable Z is ? ? µ = X Z µµµ = 2 ??? = 1 µµµ = 5 µµµµ = 0 ??? = 3 ??? = 6
The normal curve is a hypothetical distribution of scores that is widely used in psychological testing The normal curve is a symmetrical distribution of scores with an equal number of scores above and below the midpoint Given that the distribution of scores is symmetrical (i e , an equal number of scores actually are above and below the
3 Logarithmic Transformation, Log-Normal Distribution 18 Back to Properties Multiplicative“Hypothesis ofElementary Errors”: If random variation is theproductof several random effects, a log-normal distribution must be the result Note: For “many small” effects, the geometric mean will have a small ? approx normalANDlog-normal
through : through : through : through : through : through : through : through : through : through : through
We first convert the problem into an equivalent one dealing with a normal variable For example, F(0) = 5; half the area of the standardized normal curve lies to
5 1 Introduction to Normal Distributions and the Standard Example: Using The Standard Normal Table To transform a standard z-score to a data value x in a
This is an example of a continuous probability distribution (as opposed to the common practice is to convert everything to a standard normal distribution and
the mean of the normal distribution and a is its standard deviation example is due to Sim6on Denis Poisson (1781-1840) who, as early as 1824, Poisson's work by standardizing X , thus transforming the problem into finding a probability