z score table for standard normal distribution

To find the p-value to assess whether the sample differs from the population, you calculate the area under the curve above or to the right of your z-score. This means that your sample’s mean sleep duration is higher than about 98.74% of the population’s mean sleep duration pre-lockdown. The table tells you that the area under the curve up to or below your z-score is 0.9874. To find the probability of your sample mean z-score of 2.24 or less occurring, you use the z-table to find the value at the intersection of row 2.2 and column +0.04. FormulaĪ z-score of 2.24 means that your sample mean is 2.24 standard deviations greater than the population mean. To compare sleep duration during and before the lockdown, you convert your lockdown sample mean into a z-score using the pre-lockdown population mean and standard deviation. Then, you find the p-value for your z-score using a z-table.First, you calculate a z-score for the sample mean value.To assess whether your sample mean significantly differs from the pre-lockdown population mean, you perform a z -test: You collect sleep duration data from a sample during a full lockdown.īefore the lockdown, the population mean was 6.5 hours of sleep. Let’s walk through an invented research example to better understand how the standard normal distribution works.Īs a sleep researcher, you’re curious about how sleep habits changed during COVID-19 lockdowns. Step-by-step example of using the z-distribution That means it’s likely that only 6.3% of SAT scores in your sample exceed 1380. Position or shape (relative to standard normal distribution) A small standard deviation results in a narrow curve, while a large standard deviation leads to a wide curve. The standard deviation stretches or squeezes the curve. Increasing the mean moves the curve right, while decreasing it moves the curve left. The mean determines where the curve is centred. In the standard normal distribution, the mean and standard deviation are always fixed.Įvery normal distribution is a version of the standard normal distribution that’s been stretched or squeezed and moved horizontally right or left. However, a normal distribution can take on any value as its mean and standard deviation.

Normal distribution vs the standard normal distributionĪll normal distributions, like the standard normal distribution, are unimodal and symmetrically distributed with a bell-shaped curve. You can calculate the standard normal distribution with our calculator below. Frequently asked questions about the standard normal distribution.Step-by-step example of using the z-distribution.Use the standard normal distribution to find probability.Normal distribution vs the standard normal distribution.Standard normal distribution calculator.

Z score table for standard normal distribution