Question

How can we assess differences in quality or performance by simply comparing z values under a standard normal curve? (Examine the formula to compute standard z-scores).

Answer 1

The smaller the z number, the smaller the variance and the closer to the mean the parts are will give you a better capability value. Notice that, it involves both the mean and the standard deviation. Recall that the mean of the data collection is not entirely adequate to describe the data. We need the standard deviation as well.

Normal distribution may have different standard deviations and means however; they all have a bell curve shape where the mean is at the greatest height. The tails of the normal distribution are asymptotic, indefinitely decreasing but never touches the x axis. The normal distribution can be characterized as either distribution of data points within a population of scores or the theoretical distribution of a sample statistic such as a mean.

A normal distribution that is standardized, meaning the mean is 0 and standard deviation is 1, is called a standard normal distribution. This represents a distribution of z scores. Converting values such as a sample mean to z scores doesn't change the shape of the distribution. By converting normal distributed values into z scores we can determine the probabilities of specific ranges of scores by either using technology or the standard normal distribution table. It is not appropriate to use the z table to find the probabilities unless the shape of the distribution is close to the normal distribution.

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