Which of the following statements are NOT correct about Standard Normal Distribution?

(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.

(B) The Standard Normal variate (Z) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.

(C) The Z-score is negative if the data point lies above the mean, and positive if it lies below the mean.

(D) There is a 95.45 % probability of randomly selecting a score between $\mu - \sigma$ and $\mu + \sigma$, when $\sigma$ is standard deviation and $\mu$ is mean.

Choose the correct answer from the options given below:

Statement (A): The probability curve of the Standard Normal Distribution is a bell-shaped curve.

This is correct. The standard normal distribution has a symmetric, bell-shaped curve (Gaussian curve).

Statement (B): The Standard Normal variate (Z) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.

This is correct. The Z-score formula is:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations a data point is from the mean.

Statement (C): The Z-score is negative if the data point lies above the mean, and positive if it lies below the mean.

This is incorrect. The statement is backwards:

Z-score is positive when the data point is above the mean

Z-score is negative when the data point is below the mean

Statement (D): There is a 95.45% probability of randomly selecting a score between $\mu - \sigma$ and $\mu + \sigma$, when $\sigma$ is standard deviation and $\mu$ is mean.

This is incorrect. The statement assigns the wrong percentage to the wrong range.

The empirical rule states:

Within 1 standard deviation ($\mu \pm \sigma$): approximately 68% probability

Within 2 standard deviations ($\mu \pm 2\sigma$): approximately 95.45% probability

Within 3 standard deviations ($\mu \pm 3\sigma$): approximately 99.7% probability

Statement (D) incorrectly assigns the 95.45% probability to 1 standard deviation when it actually applies to 2 standard deviations.

Statements (C) and (D) are NOT correct.