Best Answer

The normal distribution is symmetric about its mean; it increases from an asymptote with the x-axis below the mean until the mean whereupon it decreases until another asymptote with the x-axis the same distance above the mean. (This is not a linear increase/decrease, but a "bell" shape.)

As the distribution is symmetric about its mean, only tables up to the mean need be calculated/given in a table. The area under the curve between any two points can then be calculated.

For a normal distribution with mean µ and standard deviation σ, a z value is calculated for a given point x:

z = (x - µ) / σ

This z value is then used to look up the area in the given "half" tables, giving the area (probability) of the value lying between the mean and the given z value. If negative, z is below the mean, but for the table, the sign is ignored.

This can be expressed as:

area = normal(|z|)

where normal(z) is the value in the normal table at the given (positive) z value.

To calculate the area between two points (ie the probability that a value lies between two given values), their corresponding z values (z₁ and z₂) are first calculated and then combined viz:

Almost all of the normal distribution lies between ±4 standard deviations of the mean.

As the distribution is symmetric about its mean, only tables up to the mean need be calculated/given in a table. The area under the curve between any two points can then be calculated.

For a normal distribution with mean µ and standard deviation σ, a z value is calculated for a given point x:

z = (x - µ) / σ

This z value is then used to look up the area in the given "half" tables, giving the area (probability) of the value lying between the mean and the given z value. If negative, z is below the mean, but for the table, the sign is ignored.

This can be expressed as:

area = normal(|z|)

where normal(z) is the value in the normal table at the given (positive) z value.

To calculate the area between two points (ie the probability that a value lies between two given values), their corresponding z values (z₁ and z₂) are first calculated and then combined viz:

- If they are both on the same side of the mean (ie z₁ and z₂ have the same sign) then the area is given by:

- If they are on opposite sides of the mean (ie z₁ and z₂ have different signs) then the area is given by:

Almost all of the normal distribution lies between ±4 standard deviations of the mean.

Study guides

☆☆

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

Write your answer...

Submit

Still have questions?

Related questions

A bell shaped probability distribution curve is NOT necessarily a normal distribution.

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

True * * * * * No. The Student's t-distribution, for example, is also bell shaped.

The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.

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

No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.

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

what is density curve

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.

I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.

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.

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.

People also asked