![]() ![]() For the normal distribution, we know that the mean is equal to median, so half (50%) of the area under the curve is above the mean and half is below, so P(BMI < 29)=0.50. For any probability distribution, the total area under the curve is 1. ![]() To compute probabilities from normal distributions, we will compute areas under the curve. It is possible to have BMI values below 11 or above 47, but extreme values occur very infrequently. The mean (μ = 29) is in the center of the distribution, and the horizontal axis is scaled in increments of the standard deviation (σ = 6) and the distribution essentially ranges from μ - 3 σ to μ + 3σ. The standard deviation gives us a measure of how spread out the observations are. BMI in MalesĬonsider body mass index (BMI) in a population of 60 year old males in whom BMI is normally distributed and has a mean value = 29 and a standard deviation = 6. ![]() There are also very useful tables that list the probabilities. ![]() ( π is a constant = 3.14159, and e is a constant = 2.71828.) Normal probabilities can be calculated using calculus or from an Excel spreadsheet (see the normal probability calculator further down the page. Where μ is the population mean and σ is the population standard deviation. If we have a normally distributed variable and know the population mean (μ) and the standard deviation (σ), then we can compute the probability of particular values based on this equation for the normal probability model:
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