Determining a Normal Distribution
Determining whether a variable has a normal distribution when working with probabilities is critical. There are several methods for determining whether a variable has a normal distribution. One common method is to graph the data with a histogram and visually assess whether the distribution is roughly bell-shaped (Black, 2019). A normal probability plot, which plots the observed values against the expected values from a normal distribution, is another method. If the points on the plot follow a straight line, the data is probably normally distributed.
The mean (mu) and standard deviation (sigma) parameters determine the shape of the normal distribution. On the one hand, the mean determines the center of the distribution. On the hand, the standard deviation is involved in determining the distribution’s spread (Shi et al., 2020). The normal distribution is symmetric around mu, with about 68 percent of the data ranging within one sigma of the mean and about 95 percent within two sigmas of the mean.
If the distribution of a random variable is normal, it is said to be normally distributed. In other words, if the values of a random variable cluster around the mean and are symmetrically distributed around it, it is normally distributed.
The mean (mu) is known as a measure of location because it represents the distribution’s center. In particular, it is the point at which the distribution is symmetrically clustered.
Because it represents the amount of variability or spread in the data, the standard deviation (sigma) is known as a measure of spread or dispersion. It determines how far the data values deviate from the mean.
Studying the equation for the graph of the normal distribution tells us several important things about the distribution. To begin, the equation demonstrates that the distribution is symmetric around the mean (mu) (Black, 2019). Second, it demonstrates that the standard deviation (sigma) determines the spread of the distribution. Finally, it includes a formula for calculating the likelihood of seeing a specific value or range of values in the distribution.
References
Black, K. (2019). Business Statistics: For Contemporary Decision Making. In Google Books (10th ed.). John Wiley & Sons.
Shi, J., Luo, D., Weng, H., Zeng, X., Lin, L., Chu, H., & Tong, T. (2020). Optimally estimating the sample standard deviation from the five‐number summary. Research Synthesis Methods. https://doi.org/10.1002/
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Question 
WEEK 3: DETERMINING A NORMAL DISTRIBUTION
When trying to determine probabilities, one must first assess whether the variable would have a normal distribution. Using the tools from this course, what are some methods that could be used to determine whether a variable has a normal distribution?
Determining a Normal Distribution
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Mar 13
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Robert Davy
Class, Welcome to the Week 3 graded discussion area. We will be talking about normal distributions this week. When trying to determine probable
Class,
Welcome to the Week 3 graded discussion area. We will be talking about normal distributions this week.
When trying to determine probabilities, one must first assess whether the variable would have a normal distribution.
Using the tools from this course, what are some methods that could be used to determine whether a variable has a normal distribution?
What determines the shape of the normal distribution?
What does it mean that a random variable is normally distributed?
Why is the mean \mu called a measure of location?
Why is the standard deviation \sigma called a measure of spread/dispersion?
What do we learn by studying the equation for the graph of the normal distribution? \begin{equation*} f(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \end{equation*}
I look forward to another great week of discussions!
NB: Directly related to my previous order.
Reference:
Business statistics, Ken Black