Expression for normal distribution

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Thread starter dekra2000
Start date Nov 1, 2018
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Distribution Expression Normal Normal distribution

In summary, the expression for normal distribution is given by the probability density function (PDF) of the normal distribution. The mean (μ) represents the center point of the curve and the most probable value, while the standard deviation (σ) measures the spread of the data from the mean. Normal distribution is commonly used in statistics to model and analyze continuous data, calculate probabilities, and make predictions. The 68-95-99.7 rule is a commonly used rule that states approximately 68%, 95%, and 99.7% of the data falls within one, two, and three standard deviations of the mean, respectively. It is also known as the empirical rule or the 3-sigma rule.

Nov 1, 2018

dekra2000

Write an expression for normal distribution for the data: Measured values are: 4,393; 4,372; 4,381; 4,373 and 4,401

thanks for help

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Nov 1, 2018

Greg

Gold Member

MHB

Re: please help to solve

Hi dekra2000 and welcome to MHB!

Any thoughts on how to begin?

What is the expression for normal distribution?

The expression for normal distribution is given by the probability density function (PDF) of the normal distribution, which is:

f(x) = (1/√(2πσ^2)) * e^(-1/2((x-μ)/σ)^2)

What does μ represent in the expression for normal distribution?

μ represents the mean or average of the distribution. It is the center point of the curve and indicates the most probable value.

What does σ represent in the expression for normal distribution?

σ represents the standard deviation of the distribution. It measures how spread out the data is from the mean. A smaller σ indicates a narrower curve and a larger σ indicates a wider curve.

How is normal distribution used in statistics?

Normal distribution is commonly used in statistics to model and analyze continuous data. It is used to calculate probabilities and make predictions about a population based on a sample. It is also used in hypothesis testing and to determine confidence intervals.

What is the 68-95-99.7 rule in normal distribution?

The 68-95-99.7 rule is a commonly used rule of thumb in normal distribution. It states that approximately 68% of the data falls within one standard deviation (σ) of the mean (μ), 95% falls within two σ of the mean, and 99.7% falls within three σ of the mean. This rule is also known as the empirical rule or the 3-sigma rule.