Final answer:
A normal probability plot is used to test distribution for normalcy by indicating whether data points form an approximate straight line according to the standard normal distribution. The standard normal distribution is a special case with a mean of 0 and standard deviation of 1. Z-tables are used to find probabilities related to the standard normal distribution by using z-scores.
Step-by-step explanation:
A normal probability plot is used to test distribution for normalcy. It is a graphical tool, which plots the data points against a theoretically normal distribution in such a way that the points should form an approximate straight line if the data is normally distributed. Deviations from this straight line suggest that the data may not be normally distributed.
The standard normal distribution, denoted as Z ~ N(0, 1), is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. The values on the x-axis of a normal probability plot are the standardized values or z-scores. A z-score indicates how many standard deviations a data point is from the mean.
To determine the area between two normal curve values or to find the z-scores corresponding to an area under a normal curve, one can use a z-table. The z-table shows the area under the curve to the left of a given z-score. By finding the z-score in the z-table, one can deduce probabilities related to the standard normal distribution (for example, the probability that a value is less than a certain amount).