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The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.

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โˆ™ 2009-09-26 22:35:17
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Q: Which normal distribution is also the standard normal curve?
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What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

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.

If a probability distribution curve is bell-shaped then this is a normal distribution?

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

If the tails of the normal distribution curve are infinitely long. Is it True or False that the total area under the curve is also infinite?

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.

Why Normal distribution is better then other distributions in statistics?

The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.

What is the meaning of normal distribution with examples?

According to the Central Limit Theorem, if you take measurements for some variable from repeated samples from any population, the mean values have a probability distribution which is known as the Gaussian distribution. Because of the fact that it is found often it is also called the Normal distribution. It is a symmetric distribution which is fully determined by two parameters: the mean and variance (or standard deviation). It is also sometimes referred to as the bell curve although I have yet to see a bell that stretches out at its bottom towards infinity!The normal distribution can be used for the heights or masses of people, for examination scores.

What are the types of normal distribution?

Generally, when we refer to the normal distribution, it is the standard, univariant normal distribution. We don't have a normal type 1, type 2, etc. However, there are closely related distributions, the truncated normal and the multivariant normal. A truncated multivariant normal would also be possible. See related links.

How much is 84 percentile equals mean plus 1 standard deviation or mean plus 1.4 standard deviation. Can you give me reference also please?

The cumulative probability up to the mean plus 1 standard deviation for a Normal distribution - not any distribution - is 84%. The reference is any table (or on-line version) of z-scores for the standard normal distribution.

What is the sketch for a normal distribution?

The normal distribution is a bell shaped curve. Properly normalized, the area under the curve is 1.0. Start by drawing axes. The Y axis is probability, peaking at 0.4, crossing the X axis at the mean, and the X axis is standard deviation. Draw points (-3, 0.01), (-2, 0.05), (-1, 0.25), (0, 0.4), (+1, 0.25), (+2, 0.05), (+3, 0.01). These are all approximations. Connect the dots, understanding that the curve is asymptotic to the X axis.For a better picture, as well as an explanation, please see the related link below. This picture also shows you the percentage each area, grouped by standard deviation, or sigma, is. The normal distribution is the second picture on the right. Scroll up to see the picture, call "Normal Distribution".

What is having one side of the distribution looking the same as the other side?

A normal distribution of data is one in which the majority of data points are relatively similar, meaning they occur within a small range of values with fewer outliers on the high and low ends of the data range. When data are normally distributed, plotting them on a graph results a bell-shaped and symmetrical image often called the bell curve. In such a distribution of data, mean, median, and mode are all the same value and coincide with the peak of the curve. However, in social science, a normal distribution is more of a theoretical ideal than a common reality. The concept and application of it as a lens through which to examine data is through a useful tool for identifying and visualizing norms and trends within a data set. Properties of the Normal Distribution One of the most noticeable characteristics of a normal distribution is its shape and perfect symmetry. If you fold a picture of a normal distribution exactly in the middle, you'll come up with two equal halves, each a mirror image of the other. This also means that half of the observations in the data falls on either side of the middle of the distribution. The midpoint of a normal distribution is the point that has the maximum frequency, meaning the number or response category with the most observations for that variable. The midpoint of the normal distribution is also the point at which three measures fall: the mean, median, and mode. In a perfectly normal distribution, these three measures are all the same number. In all normal or nearly normal distributions, there is a constant proportion of the area under the curve lying between the mean and any given distance from the mean when measured in standard deviation units. For instance, in all normal curves, 99.73 percent of all cases fall within three standard deviations from the mean, 95.45 percent of all cases fall within two standard deviations from the mean, and 68.27 percent of cases fall within one standard deviation from the mean. Normal distributions are often represented in standard scores or Z scores, which are numbers that tell us the distance between an actual score and the mean in terms of standard deviations. The standard normal distribution has a mean of 0.0 and a standard deviation of 1.0. Examples and Use in Social Science Even though a normal distribution is theoretical, there are several variables researchers study that closely resemble a normal curve. For example, standardized test scores such as the SAT, ACT, and GRE typically resemble a normal distribution. Height, athletic ability, and numerous social and political attitudes of a given population also typically resemble a bell curve. The ideal of a normal distribution is also useful as a point of comparison when data are not normally distributed. For example, most people assume that the distribution of household income in the U.S. would be a normal distribution and resemble the bell curve when plotted on a graph. This would mean that most U.S. citizens earn in the mid-range of income, or in other words, that there is a healthy middle class. Meanwhile, the numbers of those in the lower economic classes would be small, as would the numbers in the upper classes. However, the real distribution of household income in the U.S. does not resemble a bell curve at all. The majority of households fall into the low to the lower-middle range, meaning there are more poor people struggling to survive than there are folks living comfortable middle-class lives. In this case, the ideal of a normal distribution is useful for illustrating income inequality.โ€‹

Is normal distribution also a probability distribution?

Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.

What is a normal data set?

A normal data set is a set of observations from a Gaussian distribution, which is also called the Normal distribution.

What are the advantages and disadvantages of frequency curve?

A frequency curve has a major disadvantage of not showing the exact values of the distribution. it is also difficult to compare different data sets. A frequency curve has the greatest advantage of showing the skewness of the distribution that is whether it is positively skewed, negatively and symmetric distribution.

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