Match List I with List II

List I (Z-distribution)	List II (Characteristics)
A. Mean	I. Observed value (x) > mean
B. Standard Deviation	II. Observed value (x) < mean
C. Positive Z-value	III. 0
D. Negative Z-value	IV. 1

Choose the correct answer from the options given below:

Correct option is D

Introduction

The standard normal Z) distribution is a normal distribution standardised to have a mean of zero and a standard deviation of one.

The Z-score expresses how far, and in which direction, an observation lies from the mean in units of standard deviation, allowing values from any normal distribution to be compared on a common scale.

Information Booster

The Z-distribution is obtained by applying the standardisation transformation Z = (x − μ)/σ to a normal variable, which repositions and rescales the distribution to a fixed, universal form.
A. Mean → III (0): By definition, the standard normal distribution is centred so that its mean equals zero. When the transformation Z = (x − μ)/σ is applied, the population mean μ maps exactly to the origin, because substituting x = μ gives Z = 0.

This is why the Z-curve is always symmetric about zero, with equal probability on either side.
B. Standard Deviation → IV (1): The Z-distribution is scaled so that its standard deviation equals one. Dividing the deviation (x − μ) by σ normalises the spread, so one unit of Z corresponds to exactly one standard deviation of the original distribution.

This unit standard deviation is what makes Z-tables universally applicable regardless of the original data's scale.
C. Positive Z-value → I (Observed value x > mean): A positive Z-score arises only when the numerator (x − μ) is positive, which happens when the observed value x exceeds the mean μ.

Positive Z-values therefore lie to the right of the centre on the standard normal curve, indicating above-average observations.
D. Negative Z-value → II (Observed value x < mean): A negative Z-score occurs when (x − μ) is negative, meaning x is smaller than the mean. Negative Z-values lie to the left of the centre, representing below-average observations.
Together these four properties define the fundamental architecture of the Z-distribution: a mean of 0, a standard deviation of 1, and a sign convention where the algebraic sign of Z immediately reveals whether an observation sits above or below the mean.

This structure is what allows probabilities and percentiles to be read directly from standard normal tables.