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What else can I help you with?
Does a population have to be normally distributed in order to use the chi-square distribution?
No, but the approximation is better for normally distributed variables.
What percentage of the normally distributed population lies within the plus or minus one standard deviation of the population mean?
68.2%
What does it mean for a population to be normally distributed?
A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
Why do population follow normal distribution?
The form of this question incorportates a false premise. The premise is that the data are normally distributed. Actually, is the sample mean which, under certain circumstances, is normally distributed.
What is the difference between a normal distribution and a standard normal distribution?
when you doesnt have information about the real mean of a population and use the estimation of mean instead of the real mean , usually you use t distribution instead of normal distribution. * * * * * Intersting but nothing to do with the question! If a random variable X is distributed Normally with mean m and standard deviation s, then Z = (X-m)/s has a standard Normal distribution. Z has mean 0 and standard deviation = 1 (or Variance = sd2 = 1).
What will the sampling distribution of the mean be if a population is normally distribution?
Also normally distributed.
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.
When the population standard deviation is known the sample distribution is a?
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
Does a population have to be normally distributed in order to use the chi-square distribution?
No, but the approximation is better for normally distributed variables.
What percentage of the normally distributed population lies within the plus or minus one standard deviation of the population mean?
68.2%
Can the variance of a normally distributed random variable be negative?
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.
What does it mean for a population to be normally distributed?
A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
What is the formula to convert normal distribution to the standard normal distribution?
If a variable X, is distributed Normally with mean m and standard deviation s thenZ = (X - m)/s has a standard normal distribution.
Is a normally distributed variable needed to have a normally distributed sampling distribution.?
Yes, it is.
What are some examples of abnormal and normal distribution in statistics?
IQ is normally distributed in the general population. Age is not.
Why is the central limit theorem an important idea for dealing with a population not normally distributed?
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
Will the sampling distribution of x ̅ always be approximately normally distributed?
The sampling distribution of the sample mean (( \bar{x} )) will be approximately normally distributed if the sample size is sufficiently large, typically due to the Central Limit Theorem. This theorem states that regardless of the population's distribution, the sampling distribution of the sample mean will tend to be normal as the sample size increases, generally n ≥ 30 is considered adequate. However, if the population distribution is already normal, the sampling distribution of ( \bar{x} ) will be normally distributed for any sample size.
