Which of the following are the properties of normal distribution?

Choose the correct answer from the options given below

Correct option is B

Normal distribution was discovered by De Moivre in 1733. It is approximate to the binomial distribution. it is also known as a Gaussian distribution in which values are randomly distributed
Properties of Normal distribution.
 Symmetry:
· The normal distribution curve is perfectly symmetrical around the mean (μ\muμ).
· This symmetry implies that the mean, median, and mode of the distribution are all equal.
 Bell-Shaped Curve:
· The graph of the normal distribution forms a bell-shaped curve.
· It has a single peak at the mean, indicating the most likely value.
 Mean, Median, and Mode:
· In a normal distribution, the mean (μ), median, and mode are identical and located at the center of the distribution.
 Unimodal:
· The normal distribution has only one peak, making it unimodal.
 Asymptotic:
· The tails of the normal distribution extend indefinitely and approach, but never touch, the horizontal axis.
 Defined by Two Parameters:
· A normal distribution is fully characterized by its:
· Mean (μ): Determines the location of the center.
· Standard Deviation (σ): Determines the spread or width of the distribution.
 Empirical Rule (68-95-99.7 Rule):
· Approximately:
· 68% of the data lies within 1 standard deviation (μ±σ).
· 95% of the data lies within 2 standard deviations (μ±2σ).
· 99.7% of the data lies within 3 standard deviations (μ±3σ).
 Standard Normal Distribution:
· A normal distribution with a mean of 0 and a standard deviation (σ) of 1.
· Standard normal values are also called z-scores, representing the number of standard deviations a value is from the mean.
 Area Under the Curve:
· The total area under the curve equals 1, representing the entire probability distribution.
 Independent of Scale:
· Scaling or shifting a normal distribution does not change its shape. However, it alters the mean and standard deviation.
Hence, only options (B), (C) and (E) are correct.