The relationship between the standard normal random variable z and normal random variable X is that :

(A) Only the standard normal variable Z is continuous.
(B) The standard normal variable Z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
(C) The values of the standard normal random variable Z cannot be negative.
(D) The values of the normal random variable X cannot be negative.

(B) The standard normal variable Z counts the number of standard deviations that the value of the normal random variable X is away from its mean

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Positive z-score: Above the mean

Negative z-score: Below the mean

All variables are continuous.

X can be positive or negative, just like Z

So the correct answer is:

(B) The standard normal variable Z counts the number of standard deviations that the value of the normal random variable X is away from its mean

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