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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 mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
Which distribution function has equal mean and variance?
The exponential distribution and the Poisson distribution.
What is the sampling distribution when the standard deviation is known?
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
Can a standard deviation of a sample be equal to a standard deviation of a population?
Yes
If the outcomes of a random variable follow a Poisson distribution then their?
means equal the standard deviation
Area to the left of the mean in a normal distribution is equal to?
One standard deviation
What are the median and mode of a normal distribution if the mean is 22 and the standard deviation is 4?
The mean, median, and mode of a normal distribution are equal; in this case, 22. The standard deviation has no bearing on this question.
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 standard error of the sampling distribution equal to when you do not know the population standard deviation?
You calculate the standard error using the data.
Which distribution function has equal mean and variance?
The exponential distribution and the Poisson distribution.
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.
What is the sampling distribution when the standard deviation is known?
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
Are the mean and variance equal in the poisson distribution?
yes
Is the middle spread that is the middle 50 percent of the normal distribution is equal to one standard deviation?
false
True or false a distribution of sample means is normally distributed with a mean equal to the population mean and standard deviation equal to the standard error of the mean?
True.
Can a standard deviation of a sample be equal to a standard deviation of a population?
Yes
