For the value of c that validates P(z < c) = 0.5851, enter the Table Of Proportions Of Area Under The Standard Normal Curve with 0.5851 as the "argument" or value of P that is to be linked to c.
The Table shows that z-values of 0.21 and 0.22 give values of P equal to 0.5832 and 0.5871, respectively. Since 0.5851 falls between these two values, an interpolation can be reached by equating
(0.5851 − 0.5832) ÷ (0.5871 − 0.5832) to x ÷ (0.22 − 0.21). That is, 19/39 = x/0.01 or x = 0.004871794872.
Then add x = 0.004871794872 to 0.21 to obtain c = 0.214871794872.
Feeding c = 0.214871794872 into a highly accurate, Calculus-based program on a Casio Programmable Calculator will return 0.08506636212, which when added to 0.5 yields P(z < 0.214871794872) equal to 0.58506636212 ≈ 0.5851.
