Then look up the value for this standardized value. So same idea but this starts at negative, a z-score of negative 3. To use this table with a non-standard normal distribution (either the location parameter is not 0 or the scale parameter is not 1), standardize your value by subtracting the mean and dividing the result by the standard deviation. And we actually go to the first part of the z-table. Therefore P ( в€’ 5.22 < Z < 2.15 ) = 0.9842 в€’ 0.0000 = 0.9842 And so to figure out the proportion that is less than that, this red area right over here, we go back to our z-table. We can see from the first line of the table that the area to the left of в€’5.22 must be so close to 0 that to four decimal places it rounds to 0.0000.

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 в€’5.22 is too far to the left on the number line to be in the table. If you have a set of normally distributed data with a different mean and standard distribution, you can transform it into standard form with the scaling equation (X-)/ Z. Therefore P ( 1.13 < Z < 4.16 ) = 1.0000 в€’ 0.8708 = 0.1292 Z-score tables are based on a normal distribution that has a mean of 0 and a standard deviation of 1. 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. 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. Standard Normal Cumulative Probability Table. 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. Correct answer - For a standard normal distribution, find the approximate value of P (z less-than-or-equal-to 0.42).

Negative standard normal table