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 $μ - σ$ and $μ + σ$, when $σ$ is standard deviation and $μ$ is mean.

Choose the correct answer from the options given below:

(C) and (D) only

The correct answer is Option (4) → (C) and (D) only

(A) The standard normal curve is bell-shaped → correct. By definition, the probability density curve of a normal distribution is symmetric and bell-shaped.

(B) Z-score gives distance from mean in standard deviation units → correct. he formula $Z = \frac{x - \mu}{\sigma}$ measures exactly how many standard deviations an observation is from its mean.

(C) Z-score is negative if the value is above mean and positive if below mean → incorrect, it is positive above mean and negative below mean.

(D) Probability between $\mu-\sigma$ and $\mu+\sigma$ is about $68.27\%$, not $95.45\%$ → incorrect. 95.45% corresponds to the interval μ ± 2σ.

Final answer: (C) and (D)