Want this question answered?

Q: Why is only one normal table need to find any probability under the normal curve?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

The area under the normal curve is ALWAYS 1.

In statistics you can find the area under a curve to establish what to expect between two input numbers. If there is a lot of area under the curve the graph is tall and there is a higher probability of things occurring there than when the graph is low.

A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.

The area under a normal distribution is one since, by definition, the sum of any series of probabilities is one and, therefore, the integral (or area under the curve) of any probability distribution from negative infinity to infinity is one. However, if you take an interval of a normal distribution, its area can be anywhere between 0 and 1.

By standard practice, the normal distribution curve should be normalized so that the area under the curve is 1. This results in a height, at the mean, of about 0.4, i.e. the probability of a sample value being equal to the mean is 40 percent. The width of the normal distribution curve is infinite, as the tails are asymptotic to the X axis. It is easier to understand that the +/- one sigma area is 68.2 percent, the +/- two sigma area is 95.4 percent, and the +/- three sigma area is 99.6 percent.

Related questions

A normalized probability distribution curve has an area under the curve of 1.Note: I said "normalized", not "normal". Do not confuse the terms.

The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.

Please see the link under "legitimate probability density function".

Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.

100%. And that is true for any probability distribution.

False. A normalized distribution curve (do not confuse normalized with normal), by definition, has an area under the curve of exactly 1. That is because the probability of all possible events is also always exactly 1. The shape of the curve does not matter.

This is the standard normal curve. To the left P(X<x) therefore to the right is P(X>x). Therefore this means that to calculate the probability look up the Z score on the standard normal table. Then P(X>x) = 1-P(X<x). This is because the curve is symmetrical arounds its mean.

If the question is to do with a probability distribution curve, the answer is ONE - whatever the values of mu and sigma. The area under the curve of any probability distribution curve is 1.

The area under the standard normal curve is 1.

The area under the normal curve is ALWAYS 1.

the standard normal curve 2

The area under the normal distribution curve represents the probability of an event occurring that is normally distributed. So, the area under the entire normal distribution curve must be 1 (equal to 100%). For example, if the mean (average) male height is 5'10" then there is a 50% chance that a randomly selected male will have a height that is below or exactly 5'10". This is because the area under the normal curve from the left hand side up to the mean consists of half of the entire area of the normal curve. This leads us to the definitions of z-scores and standard deviations to represent how far along the normal curve a particular value is. We can calculate the likelihood of the value by finding the area under the normal curve to that point, usually by using a z-score cdf (cumulative density function) utility of a calculator or statistics software.