To find the probability of a z score in Excel, use the function =NORM.S.DIST(z, TRUE), where z is your z score. This function calculates the cumulative probability from the left tail up to that z score in the standard normal distribution (mean 0, standard deviation 1). For example, if you want the probability of a z score less than -1.5, enter =NORM.S.DIST(-1.5, TRUE), and Excel will return approximately 0.07, meaning a 7% chance. This method is useful when you have standardized data and want to find the likelihood of observing a value below a certain z score.

To find a z score corresponding to a cumulative probability in the standard normal distribution, use Excel's =NORM.S.INV(probability) function. The input probability must be a left-tail probability (the area under the curve to the left of the z score). For example, if you want the z score where 58% of values lie below it, enter =NORM.S.INV(0.58), and Excel returns approximately 0.202. This means there's a 58% chance a z score is less than 0.202. If you have a right-tail probability, convert it to left-tail by subtracting from 1 before using this function.

When dealing with a normal distribution with mean and standard deviation , use Excel's =NORM.DIST(x, mean, standard_dev, TRUE) function. Here, x is the value you're interested in. This function returns the cumulative probability that a randomly selected value is less than or equal to x. For example, if baking times are normally distributed with =11 minutes and =0.76 minutes, to find the probability of baking time less than 10 minutes, use =NORM.DIST(10, 11, 0.76, TRUE). Excel will give the left-tail probability, which is about 0.09 or 9% chance.