NORMAL DISTRIBUTION

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sainigokul

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The weekly demand of a cell phone shop is following the normal distribution with
average number of cell phones sold is 200 units and it has also been found that 90% of
time the demand is lying less than 220 units.
a. Using this information find the standard deviation of the distribution.
(5 Marks)
b. Determine the lowest stock that the company should maintain so that the probability of
shortage is not higher than 5%.
 
Hi, please tell us what are the following definitions:
1. Normal distribution.
2. Average number.
3. Standard deviation.
After that tell us exactly where do you get stuck.
 
yoscar04 said:
Hi, please tell us what are the following definitions:
1. Normal distribution.
2. Average number.
3. Standard deviation.
After that tell us exactly where do you get stuck.
Click to expand...
A distribution is called normal distribution if data is concentrated mostly around the center of the graph. The graph is a bell-curve.
Average number is the sum of observation divided by total number of observation.
Standard deviation is the square root of variance which is used to find dispersion in data set
If you want to know more, visit Data Science with RiSi
 
"A distribution is called normal distribution if data is concentrated mostly around the center of the graph. The graph is a bell-curve.
Click to expand...

There is a technical definition of a Normal Distribution. It is NOT the vague impression you have stated.

A distribution is called a Normal Distribution if it meets the definition of a Normal Distribution. We can talk about "Near Normal" or "Truncated Normal" or "Asymptotic Normal" if you like, but those aren't "Normal", either. They meet other definitions.

Learn to rely on DEFINITIONS, not just impressions.
 
sainigokul said:
The weekly demand of a cell phone shop is following the normal distribution with
average number of cell phones sold is 200 units and it has also been found that 90% of
time the demand is lying less than 220 units.
a. Using this information find the standard deviation of the distribution.
(5 Marks)
b. Determine the lowest stock that the company should maintain so that the probability of
shortage is not higher than 5%.
Click to expand...
Is this part of an introductory probability course? The definitions you need should be in your book.
 
sainigokul said:
The weekly demand of a cell phone shop is following the normal distribution with
average number of cell phones sold is 200 units and it has also been found that 90% of
time the demand is lying less than 220 units.
a. Using this information find the standard deviation of the distribution.
(5 Marks)
b. Determine the lowest stock that the company should maintain so that the probability of
shortage is not higher than 5%.
Click to expand...
In order to help, we need to know what you have learned, and where you are stuck. (As you can see in this thread, there are very different levels at which we could talk about this!) Presumably you have learned something about the "z-score", and have either a table or software to find probabilities in a normal distribution; but we don't know the details of what you know.

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tkhunny said:
There is a technical definition of a Normal Distribution. It is NOT the vague impression you have stated.

A distribution is called a Normal Distribution if it meets the definition of a Normal Distribution. We can talk about "Near Normal" or "Truncated Normal" or "Asymptotic Normal" if you like, but those aren't "Normal", either. They meet other definitions.

Learn to rely on DEFINITIONS, not just impressions.
Click to expand...
So what are you telling about normality. When is a distribution called normal.. Please explain
 
shamri shamseer said:
So what are you telling about normality. When is a distribution called normal.. Please explain
Click to expand...
It is "called" Normal when it IS Normal, not just when you feel like it might be. However, don't be discouraged. It is the nature of statistics that things can still be useful when they are close enough. We call these approximations, but we don't quite fool ourselves into thinking that any form of approximation is exact. We just need to be honest about it.
 
You haven't answer the question of Dr. Peterson. People can not help you if they don't know what you know. For the time being this is the definition of one of the objects you asked. By the way, the notation is a bit old but you can get the idea of what a normal distribution is.1595920715724.png
 
That is the standard normal distribution, with mean 0 and standard deviation 1. The general normal distribution, with mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\) is given by

\(\displaystyle \frac{1}{\sigma\sqrt{2\pi}}\)\(\displaystyle e^{-\frac{(x- \mu)^2}{\sigma^2}}\).

In this problem, we are told that \(\displaystyle \mu= 200\). If 90% are less than 220, then 10% are larger than 220= 200+ 20 and, by symmetry, 10% are less than 200- 20= 180. That is, 80% lie within 20 of the mean. In the standard normal distribution, 80% lie within one standard deviation of the mean so the standard deviation here is 20.
 
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yoscar04 said:
You haven't answer the question of Dr. Peterson. People can not help you if they don't know what you know. For the time being this is the definition of one of the objects you asked. By the way, the notation is a bit old but you can get the idea of what a normal distribution is.View attachment 20680
Click to expand...
Are you aware that Shamri is not the OP, and appears to be trying to help, not asking a question?

I haven't asked Shamri any questions; my questions were to the OP, @sainigokul, who has not written back at all. And I expect the OP not to have any particular idea of the definition of the normal distribution, but to be more likely at the introductory level, where they are simply told that something is normal, and expected to apply routine methods, perhaps using a table.
 
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