# Normal distribution

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#1
You see the area under the graph what does it actually show you because I'm confused. is it the probability of getting a certain number of random variable x (e.g. the probability that you get 41 kg for a mass of something). Also when we are working this out we tend to use negative infinity and positive infinity too. how can this work i.e. the probability of the mass of something equal to negative 200. What does the numbers at the bottom show you and what does the area under the graph show you. also whats the difference between the cumulative one and the one where its equal.

Please clarify this as I feel like I am able to do the questions, but I don't really understand what it means its just memorising a method. I probably need to actually understand it for the harder questions

Thank you.
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1 year ago
#2
Areas under the graph represent probabilities. That's why the total area under the graph is 1.

On the horizontal axis will be the quantity that has a Normal distribution. For example, if we are investigating the mass of people then the quantity on the horizontal axis is mass in kg.

The normal distribution is a continuous function so the probability of any particular value is 0. For example the probability that the mass is exactly 41 kg is 0. The probability density function isn't 0. You can think of that as being the probability of the mass being close to a particular value, or a measure of how rapidly the cumulative probability is increasing.

Remember that the Normal distribution is only a model. It's often a very good model but clearly not perfect because as you point out it could suggest that a mass could be negative 200. But nearly all of the probability is within 3 standard deviations of the mean so the probability of extreme values is very low indeed.
Last edited by MarkFromWales; 1 year ago
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#3
(Original post by MarkFromWales)
Areas under the graph represent probabilities. That's why the total area under the graph is 1.

On the horizontal axis will be the quantity that has a Normal distribution. For example, if we are investigating the mass of people then the quantity on the horizontal axis is mass in kg.

The normal distribution is a continuous function so the probability of any particular value is 0. For example the probability that the mass is exactly 41 kg is 0. The probability density function isn't 0. You can think of that as being the probability of the mass being close to a particular value, or a measure of how rapidly the cumulative probability is increasing.

Remember that the Normal distribution is only a model. It's often a very good model but clearly not perfect because as you point out it could suggest that a mass could be negative 200. But nearly all of the probability is within 3 standard deviations of the mean so the probability of extreme values is very low indeed.
So its like saying the area under the graph up to 41 is the probability of having a mass of -infinity to 41kg (i.e. the probability of all of those weights cumulatively added together right?)
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1 year ago
#4
(Original post by fares22)
So its like saying the area under the graph up to 41 is the probability of having a mass of -infinity to 41kg (i.e. the probability of all of those weights cumulatively added together right?)
Yes, that's right. In other words the probability of the mass being less than 41 kg.
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