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Normal distribution is symmetric with single peak.Does this mean that all distibutions are normal?
No, not all distributions are symmetrical, and not all distributions have a single peak.
Why is it correct to say a normal distribution and the standard normal distribution?
A normal distribution refers to any bell-shaped distribution characterized by its mean and standard deviation, allowing for a variety of shapes depending on these parameters. The standard normal distribution, however, is a specific case of a normal distribution where the mean is 0 and the standard deviation is 1. This standardization allows for easier comparison and calculation of probabilities using z-scores, which represent the number of standard deviations a data point is from the mean. Thus, while all standard normal distributions are normal distributions, not all normal distributions are standard normal distributions.
True or false two normal distributions that have the same mean are centered at the same place regardless of the relationship between their standard deviation?
True. Two normal distributions that have the same mean are centered at the same point on the horizontal axis, regardless of their standard deviations. The standard deviation affects the spread or width of the distributions, but it does not change their center location. Therefore, even with different standard deviations, the distributions will overlap at the mean.
Are all symmetric distributions normal distributions?
No. There are many other distributions, including discrete ones, that are symmetrical.
Do t distributions have less spread than normal distributions?
I think yes or no
Why is it correct to say a normal disstrubtion and the standard normal distribution?
A normal distribution refers to a continuous probability distribution that is symmetrical and characterized by its mean and standard deviation. In contrast, the standard normal distribution is a specific case of the normal distribution where the mean is 0 and the standard deviation is 1. This standardization allows for easier comparison and calculation of probabilities using z-scores, which represent the number of standard deviations a data point is from the mean. Thus, while all standard normal distributions are normal, not all normal distributions are standard.
How many standard normal distributions are there?
Only one. A normal, or Gaussian distribution is completely defined by its mean and variance. The standard normal has mean = 0 and variance = 1. There is no other parameter, so no other source of variability.
Can the standard normal variate in normal distributions be negative?
About half the time.
In a normal distribution if the mean and the mode are both 25 what would the median be?
In a normal distribution, the mean, median, and mode are all equal. Therefore, if both the mean and the mode are 25, the median would also be 25. This property is a defining characteristic of normal distributions.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
Does this means that all symmetric distribution are normal Explain?
Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.
What does it mean normal distribution?
The Normal distribution is a probability distribution of the exponential family. It is a symmetric distribution which is defined by just two parameters: its mean and variance (or standard deviation. It is one of the most commonly occurring distributions for continuous variables. Also, under suitable conditions, other distributions can be approximated by the Normal. Unfortunately, these approximations are often used even if the required conditions are not met!
