Normal Distribution or (Gaussian) distribution in Statistics?

A Normal Distribution is also called “Gaussian Distribution” or more commonly known as “Bell Curve” as the probability distribution function plot of a normal distribution looks very like 🔔 bell-shaped.

A Normal Distribution is a univariate probability distribution, which means it is a distribution for only one random variable. Note: Multivariate normal distributions do exist but in this article, we would be talking about only univariate normal distribution.

The normal distribution is an arrangement of data points in which most values form a cluster in the middle of the range and the rest taper off symmetrically toward either extreme ends.

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Normal distribution, also known as Gaussian distribution, is a continuous probability distribution that is symmetric around its mean, μ, and characterized by its standard deviation, σ. It's often referred to as the bell curve due to its shape.

In a normal distribution:

1. The mean (μ) is the center of the distribution.
2. The standard deviation (σ) determines the spread of the distribution.
3. The distribution is symmetric around the mean.
4. The total area under the curve is 1.

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In probability theory, a normal distribution is a type of continuous probability distribution for a real-valued random variable (say X). The general form of its probability density function is

68–95–99.7 Rule for Bell Curve!

Normal distributions are very important in statistics and often they are very naturally occurring. One of the main reasons for the popularity of the Normal Distribution curve is that it occurs very commonly in most of the things we see in nature around us. For example: in finance, like the salary distribution in an office, healthcare, hydrology, height/weight distributions, grading distribution, Percentile calculations, and much more. You name it and normal distribution owns it.

Source: Blitsnap, Normal Desktop Probability Machine

To solve problems involving normal distribution, you typically follow these steps:

1. Identify the parameters: Determine the mean (μ) and standard deviation (σ) of the distribution.
2. Calculate probabilities: Use the properties of the normal distribution to calculate probabilities associated with certain events. You might be asked to find the probability of a random variable falling within a certain range, below or above a certain value, etc. You can do this using Z-scores and the standard normal distribution table or using statistical software.
3. Convert to standard normal distribution: If you're given a normal distribution problem but need to use a standard normal distribution table, you'll need to convert your values to Z-scores. The formula for Z-score is:

Where:

X is the value from the original distribution,

μ is the mean of the original distribution,

σ is the standard deviation of the original distribution.

1. Apply the standard normal distribution table or calculator: Once you've converted your values to Z-scores, you can look up probabilities associated with those Z-scores in a standard normal distribution table or use a statistical calculator.
2. Interpret the results: After calculating probabilities, interpret the results in the context of the problem.

Remember, there are various properties and formulas associated with the normal distribution, such as the 68-95-99.7 rule (Empirical Rule) which states that approximately 68%, 95%, and 99.7% of the data falls within 1, 2, and 3 standard deviations from the mean, respectively. Familiarizing yourself with these properties and formulas will help you solve normal distribution problems effectively.

Q1  Normal Distribution is symmetric is about ?

a) Variance   b) Mean   c) Standard Deviation  d)None

Q2  Area under the standard normal curve is

a) zero      b) 1.0      c) 0.5        d) ∞

Q3  In case of Normal Distribution  which is true

a)Mean = Median ≠Mode     

b)Mean ≠ Median ≠Mode     

c)Mean = Median = Mode  

d)None of above  

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