![standard normal table standard normal table](https://cdn.scribbr.com/wp-content/uploads/2020/11/z-table.png)
We can see from the first line of the table that the area to the left of −5.22 must be so close to 0 that to four decimal places it rounds to 0.0000.
![standard normal table standard normal table](https://media.cheggcdn.com/media/2f1/2f1e31ad-f97a-468a-8186-75ad3ccb28ee/phpKyM31Y.png)
Similarly, here we can read directly from the table that the area under the density curve and to the left of 2.15 is 0.9842, but −5.22 is too far to the left on the number line to be in the table. We can see from the last row of numbers in the table that the area to the left of 4.16 must be so close to 1 that to four decimal places it rounds to 1.0000. The NORM.S.DIST function can be used to determine the probability that a random variable that is standard normally distributed would be less than 0. Simply put, if an examiner asks you to find the probability. However, the table does this only when we have positive values of (z).
![standard normal table standard normal table](https://useruploads.socratic.org/6iEAaVSaT3aGP52HMzo3_z-score-02.png)
It will calculate the Excel Standard Normal Distribution function for a given value. Using the standard normal distribution table, we can confirm that a normally distributed random variable (Z), with a mean equal to 0 and variance equal to 1, is less than or equal to (z), i.e., (P(Z z)). We obtain the value 0.8708 for the area of the region under the density curve to left of 1.13 without any problem, but when we go to look up the number 4.16 in the table, it is not there. The NORM.S.DIST Function is categorized under Excel Statistical functions. We attempt to compute the probability exactly as in Note 5.20 "Example 6" by looking up the numbers 1.13 and 4.16 in the table.