![]() ![]() The probability of a score is greater than or equal to the raw score is known as a p-value. The z-score for a score x is equal to x minus the population mean μ, divided by the population standard deviation σ.Īfter you calculate the z-score for a given value, you can calculate the cumulative probability of a value being below the observation using spreadsheet software, a z-table, or a graphing calculator. The formula states that for any value of x, you can solve the probability density with the function: ![]() You can define the curve of a normal distribution using the probability density function using the population mean and standard deviation. It is not trivial to calculate the area under a normal distribution curve, but many formulas and tools have been created to simplify this task. The proportion of the area under the curve between two points indicates the probability that a score will fall within that range. The total area under the curve of a standard normal distribution is exactly equal to 1.Ĭonverting a normal distribution to a standard normal distribution allows comparing scores on distributions that have different means and standard deviations and allows you to normalize scores for decision-making purposes.įinding the area under a normal distribution bell curve is important as it allows us to calculate the probability of observing a score within a range of the distribution. It is characterized by having a mean equal to zero and a standard deviation equal to 1. While all normal distributions are symmetrical, the exact shape of the bell curve is defined by two parameters of the data: the mean and standard deviation.Ī standard normal distribution, sometimes called a z-distribution, is a special normal distribution that has been standardized by converting its values to z-scores. While a normal distribution is one of the most common probability distributions in statistics, there are also other non-normal probability distributions, such as the binomial distribution or Poisson distribution. Data that does not follow a normal distribution are called non-normal data. In some cases, a normal distribution is not possible due to sample size limitations or skewness in the data set. ![]()
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