Standard normal cumulative

TABLE 20.5.2 Standard Normal, Cumulative Probability in Rigbt-Hand Tail (for Negative Values of z, Areas Are Found by Symmetry) ... 

Figure 85. Standard normal, cumulative probability in right-hand tail (for negative values of z, areas are found by symmetry) ...

Figure 136. Standard normal, cumulative probability curve.

Table A.l (Appendix 2) gives the proportion of values, F z), that lie below a given value of z. F z) is called the standard normal cumulative distribution function. For example the proportion of values below z = 2 is F(2) = 0.9772 and the proportion of values...

Table A.1 F[z), the standard normal cumulative distribution function...

In equation 5, ( ) is the standard normal cumulative density function. The schematic representation of the FORM method is shown in Figure 1.1. 

Since the standard normal space is rotational symmetric, probability of failure can be directly obtained using the reliability index, Pj =<6(-y, where <6 is the standard normal cumulative probability function. 

The derivation of this formula is provided in Appendix 13B and Appendix 13C. Here, Fg is the standard normal cumulative distribution function and fg is the standard normal density function discussed in Appendix 12A in Chapter 12. The expected profit from ordering 0 units is evaluated in Excel using Equations 12.22,12.25, and 12.26, as follows ... 

Here, fix) is the normal density function, fs ) is the standard normal density function, and Fsi,) is the standard normal cumulative distribution function. 

Assume that the manufacturer incurs a production cost of v per unit and charges a wholesale price of c from the retailer. The retailer, in turn, sells to customers for a price of p. The retailer salvages any leftover units for sr. The manufacturer salvages any leftover units for %. If retailer demand is normally distributed, with a mean of /r and a standard deviation of a, we can evaluate the impact of a quantity flexibility contract. If the retailer orders 0 units, the manufacturer is committed to supplying Q units. As a result, we assume that the manufacturer produces Q units. The retailer purchases q units if demand D is less than q, D units if demand D is between q and Q, and Q units if demand D is greater than Q. In the following formulas, Fs is the standard normal cumulative distribution function and fs is the standard normal density function discussed in Appendix 12A in Chapter 12. We thus obtain... 

Transform the original Z data to a standard normal distribution (all work will be done in normal space). There are different techitiques for this transformation. The normal score transformation whereby the normal transform y is calculated from the original variable z as y = G- [F(z)], where G(-) is the standard normal cumulative distribution function (cdf) and F -) is the cdf of the original data. 

---