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Why is less than the same thing as less than or equal to for the normal distribution computationally in statistics?
Wiki User
∙ 8y ago
For a continuous distribution - which is what we are considering here - the probability of something being EXACTLY a specific value is zero. This is basically because there are infinite many possible values. You will only ever consider ranges of numbers, such as the probability of something being 1 and 2.
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoThe Normal distribution is continuous. As a result the probability of getting exactly a single value, X = x, is zero. If possible, this would be represented by the "area" below the point x on the Normal curve. Since there is no width to this area, its value is zero.
It follows then, Pr(X < =x) - Pr(X < x) = Pr(X = x) = 0,
or equivalently, Pr(X < =x) = Pr(X < x)
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Does mode equal median in a normal distribution?
Yes, mode equals median in a normal distribution.
What is the perfect standard normal distribution?
The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
Is the mode and median equal in a normal distribution?
Yes.
Does mode equal median in normal distribution?
Yes.
Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
What is computationally equivalent?
Arithmetically equal
Does mode equal median in a normal distribution?
Yes, mode equals median in a normal distribution.
What is the perfect standard normal distribution?
The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
What is the expected value of the standard normal distribution equal to?
The expected value of the standard normal distribution is equal to the total amount of the value. It is usually equal to it when the value works out to be the same.
Are the mean and median equal in a normal distribution?
Yes.
Is the mode and median equal in a normal distribution?
Yes.
Does mode equal median in normal distribution?
Yes.
Is total area under a normal distribution finite?
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
Why is t score equal to z score in a normal distribution?
Because as the sample size increases the Student's t-distribution approaches the standard normal.
What information do you need to calculate a probability with a normal distribution?
Only the mean, because a normal distribution has a standard deviation equal to the square root of the mean.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
True or False are the mean median and mode all equal for a normal distribution?
True. You can find many references including wikipedia on the Normal distribution on the internet.
