Normal Distribution or (Gaussian) distribution in Statistics?

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.

Watch this Youtube video on YouTube :

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.

?????????????? ??y ???????????????? (???????????????????? & ????????????????) ?????????????? for regular updates: .

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

Source: Wikipedia?


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??


?????????????? ??y ???????????????? (???????????????????? & ????????????????) ??????????????: .https://www.whatsapp.com/channel/0029VaEWKWbIiRovZpAduc0p


?????????????? ??y ?????? ?????????? ???????????????? ??????????????: https://whatsapp.com/channel/0029VaEWKWbIiRovZpAduc0p


?????????????? ??y ?????????????? ???????????????????? ???????????????????????? (??????) ???????????????? ??????????????

https://www.whatsapp.com/channel/0029Va8slQdEAKWAhXoQK13B


?????????????? ???? ???????? ?????? ?????????? ???????????????? ??????????????: https://www.whatsapp.com/channel/0029VaAUuqs4inooet3e4S3O


?????????????? ???? ?????????????? ?????????????????? & ?????????????? ?????????????? ???????????????? ??????????????:

https://www.whatsapp.com/channel/0029VaAKJBGKGGGDjcK4mw2h


?????????????? ???? ???? ?????????????? : https://lnkd.in/e4RunjP

?? ???????????? ???? ???? ?????????????????? : https://lnkd.in/ec4eDiJQ

?? 75?? ?????????????????????? ???? ?????????????? ??????????????. ?????????????????? ???? ?????????????? ?????????????? :

hashtag#statistics hashtag#leansixsigma hashtag#lean hashtag#sixsigma hashtag#leanmanufacturing hashtag#leanmanagement hashtag#leanthinking hashtag#leantraining hashtag#leantransformation hashtag#sixsigmacertification hashtag#sixsigmagreenbelt hashtag#sixsigmablackbelt hashtag#sixsigmayellowbelt hashtag#sixsigmatraining hashtag#sixsigmawhitebelt hashtag#leancertification hashtag#leansixsigmablackbelt hashtag#leansixsigmatraining hashtag#leansixsigmacertification hashtag#leansixsigmagreenbelt hashtag#leansixsigmaasia hashtag#DPU hashtag#dpmo hashtag#yeild


Carlos Mejia

Profesional

12 个月

Is always good to check and understand the core of the science.

回复

Thanks for sharing!

回复
Pierre BAYLE

Six Sigma Freelance Consultant at Sigma Solutions

1 年

I once read... "A normal distribution? I have never seen one..." - Deming

Al Smith

Retired / Management Consulting

1 年

Please at least read Wheeler & Chambers "Understanding Statistical Process Control". Once that info. sinks in continue to read the other works of Dr. Wheeler so come the end of the day you will understand the reality of industrial statistics and how FUBAR the six-sigma cult is.

要查看或添加评论,请登录

Lean Manufacturing & Six Sigma Worldwide的更多文章

社区洞察

其他会员也浏览了