# Normal distribution graph generator free online calculator

## critical value Calculator - normal distribution

You can find the result presented via a graph using our simple and free online test statistics calculator, that reflect the normal distribution and the critical value result. The level of significance, the mean and the standard deviation can be customized. For more focused results, choose two tails, left tail or right tail. Remember that the result, in the form of a graph, can be downloaded thanks to our graph generator system.

### Critical value result for z

## P-value Calculator - normal distribution

To use our free online calculator you only have to specify the z value, the mean, and the standard deviation. Select left, right, or two tails for more specific results. You will also get a graph with our free graph generator showing the normal distribution and the corresponding p-value result.

### P-value result for z

## Z score Calculator - normal distribution

You can use our free online calculator to determine a standardized z-score for any value.

Simply complete the necessary fields. Our calculator also allows you to visualize the results with our graph generator tool.

### Z-score result for z

## Z test one sample Calculator

In this calculator, you can perform a one-sample z-test to get the z-score, p-value, and critical value to help you determine whether or not your result is significant and whether the sample mean differs significantly from the mean of the population from which it is drawn. Your result can also be seen through a graph that you can download. You only need to fill in the corresponding data indicating whether a hypothesis is a left, right, or two-tailed test.

### Z-score result for z

## Z test two sample Calculator

The two sample z-test calculator performs the z-test to assess the level of significance of the differences in the means of two sets of data. You can download a graph that will show you your results. To complete the form, it is necessary to indicate the data related to the two groups, such as the mean, the standard deviation of the population and the size of the sample, and, finally, indicate whether it is a left, right, or two-tailed test.

### Z-score result for z

## Frequently asked questions regarding the normal distribution

In this section we will try to answer the most frequently asked questions related to the normal distribution (bell curve). We will try to delve into the fundamental principles behind the Gaussian distribution so that you can acquire a basic and complementary understanding. The approach that we intend to carry out is to provide useful knowledge through the most frequent questions of the students. Let's tackle problems in a simple way, providing short and clear answers.

### Questions related to the normal distribution

The formula in relation to the probability density function (pdf), for a normal random variable x, is presented as follows:

Where: μ is the mean, σ is the standard deviation, and σ² is the variance.

A normal distribution with a mean of 0 and a standard deviation of 1, is known as the standard normal distribution.

In a Gaussian distribution, the mean, median, and mode are always the same. It is a distribution that has a symmetrical shape. Due to its visual aspect or its shape, it is known as a bell. If the mean, median, and mode do not match, the statistical distribution is said to be skewed.

The normal distribution or Gaussian distribution is characterized by the following: It has the shape of a bell. It is, therefore, symmetric, since the mean, the median and the mode are equal, being located in the center of the distribution.

As for the standard normal distribution, it is a specific type of normal distribution. Where the following conditions are presented: μ=0, σ=1, also known as z distribution.

In real life, we can find examples that illustrate the normal distribution if we collect enough data on, for example, the height of women, the weight of men, or the shoe size of children between the ages of 8 and 10. We can find that the data is distributed in the form of a bell, having a certain value as the mean since a large part of the data is around the mean. Even within the chaos of the financial markets, the Gaussian distribution is used to make predictions, it is only necessary to know the mean and the standard deviation to understand the distribution of the data that make up the sample.

In a set of data, the distances between each observation and the mean are calculated using a statistical unit called the standard deviation. The standard deviation measures the level of variability or dispersion. In other words, it is used to measure the deviation of a random variable from its mean.

The z-value or the z-score are the same. It is one of the measures of relative position. If we consider a continuous random variable X, by definition a value of z describes its position relative to the number of standard deviations from the mean.

Significance level is a point in the normal distribution, it is necessary to know that point to reject or fail to reject the null hypothesis, to determine if the results are statistically significant or not.

In case of choosing our **normal distribution calculator**, you must enter the alpha value corresponding to the significance level. Generally, the most common confidence levels are: 90%, 95% and 99% (1 − α is the confidence level). Therefore, the most usual significance levels are 10%, 5% and 1% that can be entered in the calculator according to these values: 0.1, 0.05 or 0.01.

The p-value is a probability, its value is between zero and one. It is used for hypothesis testing.

As an example, in some experiment, we choose the significance level value as 0.05, in this case, the alternative hypothesis is more likely to be supported by stronger evidence when the p-value is less than 0.05 (p-value < 0.05), in case the p-value is high (p-value > 0.05), the probability of accepting the null hypothesis is also high.

The normal distribution and the Gaussian distribution are the same. We refer to a certain set of data that, due to their dispersion and distribution, are characterized by being symmetric around the mean. Its graphic form shows a figure similar to the bell, hence it is also called a bell curve.

The normal distribution is often used in statistical calculations to model real-life data. It can be used to determine the probability of a given observation occurring within the distribution, to compare values from different distributions, or to compare a value to a known standard. It is also used in hypothesis testing to determine the level of significance of the results and whether the null hypothesis can be rejected.

Yes, the calculator allows you to customize the level of significance, as well as the mean and standard deviation, by entering the desired values. This can be useful for comparing the results of different scenarios or for focusing on specific parts of the distribution.

To use the calculator to determine a standardized z-score for a value, you will need to enter the value, the mean, and the standard deviation into the calculator. The calculator will then generate the corresponding z-score, which is the measure of the distance between the value and the mean of the normal distribution, expressed in terms of standard deviations. Standardization involves converting a value to a standard form by subtracting the mean and dividing by the standard deviation, so that the resulting z-score has a mean of 0 and a standard deviation of 1.

To use the calculator to perform a one-sample **z-test**, you will need to enter the data for the sample, along with the population mean and the standard deviation of the population. The calculator will then generate the z-score, p-value, and critical value for the test, which can be used to determine whether the sample mean differs significantly from the population mean. A one-sample z-test is a statistical test used to compare the mean of a sample to a known population mean, using the normal distribution.

To use the calculator to perform a two-sample z-test, you will need to enter the data for both samples, along with the means and standard deviations of the populations. The calculator will then generate the z-score, p-value, and critical value for the test, which can be used to assess the level of significance of the differences in the means of the two samples. A two-sample z-test is a statistical test used to compare the means of two different samples, using the normal distribution.

The **p-value** is a probability that is used in hypothesis testing to determine the level of significance of the results. In the context of the normal distribution, the p-value can be used to determine whether a given observation is likely to have occurred by chance or whether it is statistically significant. A low p-value indicates that the observation is unlikely to have occurred by chance and is therefore more likely to be statistically significant.