Fortunately, all normal distributions can be converted into a single distribution, the standardized normal distribution or the z distribution, which has mean 0 and standard deviation 1. We write Z ∼ N(0, 1).
The conversion formula for any x value of a given normal distribution is:
A z-score is the number of standard deviations that a value, x, is above or below the mean.
If the value of x is less than the mean, the z score is negative.
If the value of x is more than the mean, the z score is positive.
If the value of x equals the mean, the z score is zero.
This formula allows conversion of the distance of any x value form its mean into standard deviation units. A standard z score table can then be used to find probabilities for any normal distribution problem that has been converted to z scores.
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