# standard normal distribution calculator

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Enter mean (average), standard deviation, cutoff points, and this normal distribution calculator will calculate the area (=probability) under the normal distribution curve. The calculator will generate a step by step explanation along with the graphic representation of the area you want to find. The below formula is the mathematical representation of Gaussian distribution to know what are all the input parameters are being used to find the probability of area of data range in left, right or two tailed normal distributions. The negative z-score lies on left side represents the left tail & the positive score lies on right side represents right tail of the normal or Z-distribution. As it was seen in the previous example, for a normally distribution variable $$X$$, with population $$\mu$$ and standard deviation $$\sigma$$, the z-score of a given raw score $$x$$ is computed as: Assume that you want to know how you stand in terms of weight for your whole population. Normal distribution or Gaussian distribution (according to Carl Friedrich Gauss) is one of the most important probability distributions of a continuous random variable. The answer is simple, the standard normal distribution is the normal distribution when the population mean \mu μ is 0 and the population standard deviation is \sigma σ is 1. Generally, 68.27%, 95.45% and 99.73% data observations fall around the mean between ±1σ, ±2σ and ±3σ respectively. web browser that Indeed, consider a normally distribution variable $$X$$, with population $$\mu$$ and standard deviation $$\sigma$$. The calculator will return the standard normal distribution, also known as the z-score. Specify the event you want to compute the probability for in the following form: The Standard Normal Distribution is one of the most important distributions because it allows you to compute the probabilities associated to ANY normal distribution. The simplest case of a Gaussian distribution is known as the standard normal probability distribution. Using the information provided or the formula Y = { 1/[ σ * sqrt(2π) ] } * e-(x – μ)2/2σ2 , determine the normal random variable. A smaller & larger standard deviation values represent how the data is tightly or loosely bundled around the mean accordingly. The range of data or standard normal variate x lies anywhere between -∞ and +∞. Normal Distribution is also well known by Gaussian distribution. Then, the z-score associated to your weight would be. Example to find probability of range between x, Insert this widget code anywhere inside the body tag. getcalc.com's Normal (Gaussian) Distribution calculator is an online statistics & probability tool to estimate the probability of standard normal variate range such as P(X < X1), P(X > X1), P(X < X2), P(X > X2) or P(X1 < X < X2) in left, right or two tailed distributions. To learn more about the normal distribution, go to Stat Trek's tutorial on the normal distribution. It’s a normal distribution that has a mean of 0 and standard deviation of 1. By using this normal distribution table & calculator, user may estimate what is the probability of standard normal variate range in left, right or two tailed normal distributions. Why is that?? The calculator will return the standard normal distribution, also known as the z-score. To view this video please enable JavaScript, and consider upgrading to a The answer is simple, the standard normal distribution is the normal distribution when the population mean $$\mu$$ is 0 and the population standard deviation is $$\sigma$$ is 1. How would you find the Z score of weight. In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us. You are required to calculate Standard Normal Distribution for a score above 940. The table below is a right-tail z-table.