Appendix D — Statistical Tables

NoteLearning objectives

After reading this chapter you should be able to:

• read a standard normal probability from a table to four decimal places
• read the standard normal loss functions and scale them to a demand distribution
• read cumulative Poisson probabilities and Poisson loss functions for hand work

These tables exist so that the hand computations of Chapter 7 and Chapter 8 can be worked without software. Every figure in them was generated at full precision and rounded for printing, so a value computed with a calculator may differ from the table in the last place shown. Where a hand result and a computed result disagree by more than that, the disagreement is a mistake and not a rounding.

D.1 Standard Normal Distribution

Table D.1 gives \(\Phi(z) = P\{Z \le z\}\) for a standard normal \(Z\). Read the first decimal place of \(z\) down the left column and the second across the top. For example, \(\Phi(1.64) = 0.9495\). For a negative argument use the symmetry of the density, \(\Phi(-z) = 1 - \Phi(z)\), so \(\Phi(-1.64) = 0.0505\).

Table D.1: The standard normal cumulative distribution function \(\Phi(z)\). Notice that the table runs only over non-negative \(z\), because the symmetry of the normal density makes a second half unnecessary.

\(z\)	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224
0.6	0.7257	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7517	0.7549
0.7	0.7580	0.7611	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823	0.7852
0.8	0.7881	0.7910	0.7939	0.7967	0.7995	0.8023	0.8051	0.8078	0.8106	0.8133
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.8340	0.8365	0.8389
1.0	0.8413	0.8438	0.8461	0.8485	0.8508	0.8531	0.8554	0.8577	0.8599	0.8621
1.1	0.8643	0.8665	0.8686	0.8708	0.8729	0.8749	0.8770	0.8790	0.8810	0.8830
1.2	0.8849	0.8869	0.8888	0.8907	0.8925	0.8944	0.8962	0.8980	0.8997	0.9015
1.3	0.9032	0.9049	0.9066	0.9082	0.9099	0.9115	0.9131	0.9147	0.9162	0.9177
1.4	0.9192	0.9207	0.9222	0.9236	0.9251	0.9265	0.9279	0.9292	0.9306	0.9319
1.5	0.9332	0.9345	0.9357	0.9370	0.9382	0.9394	0.9406	0.9418	0.9429	0.9441
1.6	0.9452	0.9463	0.9474	0.9484	0.9495	0.9505	0.9515	0.9525	0.9535	0.9545
1.7	0.9554	0.9564	0.9573	0.9582	0.9591	0.9599	0.9608	0.9616	0.9625	0.9633
1.8	0.9641	0.9649	0.9656	0.9664	0.9671	0.9678	0.9686	0.9693	0.9699	0.9706
1.9	0.9713	0.9719	0.9726	0.9732	0.9738	0.9744	0.9750	0.9756	0.9761	0.9767
2.0	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9812	0.9817
2.1	0.9821	0.9826	0.9830	0.9834	0.9838	0.9842	0.9846	0.9850	0.9854	0.9857
2.2	0.9861	0.9864	0.9868	0.9871	0.9875	0.9878	0.9881	0.9884	0.9887	0.9890
2.3	0.9893	0.9896	0.9898	0.9901	0.9904	0.9906	0.9909	0.9911	0.9913	0.9916
2.4	0.9918	0.9920	0.9922	0.9925	0.9927	0.9929	0.9931	0.9932	0.9934	0.9936
2.5	0.9938	0.9940	0.9941	0.9943	0.9945	0.9946	0.9948	0.9949	0.9951	0.9952
2.6	0.9953	0.9955	0.9956	0.9957	0.9959	0.9960	0.9961	0.9962	0.9963	0.9964
2.7	0.9965	0.9966	0.9967	0.9968	0.9969	0.9970	0.9971	0.9972	0.9973	0.9974
2.8	0.9974	0.9975	0.9976	0.9977	0.9977	0.9978	0.9979	0.9979	0.9980	0.9981
2.9	0.9981	0.9982	0.9982	0.9983	0.9984	0.9984	0.9985	0.9985	0.9986	0.9986
3.0	0.9987	0.9987	0.9987	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990
3.1	0.9990	0.9991	0.9991	0.9991	0.9992	0.9992	0.9992	0.9992	0.9993	0.9993
3.2	0.9993	0.9993	0.9994	0.9994	0.9994	0.9994	0.9994	0.9995	0.9995	0.9995
3.3	0.9995	0.9995	0.9995	0.9996	0.9996	0.9996	0.9996	0.9996	0.9996	0.9997
3.4	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9997	0.9998

D.2 Standard Normal Loss Functions

Table D.2 gives the density, the complementary distribution function, and the loss functions of the first three orders, defined in Section C.3.4 and Section C.3.6. To use them for a demand \(X \sim N(\mu, \sigma^{2})\) at a stock level \(x\), form \(z = (x-\mu)/\sigma\) and scale by Equation C.20: \(G^{1}(x) = \sigma\Phi^{1}(z)\), \(G^{2}(x) = \sigma^{2}\Phi^{2}(z)\) and \(G^{3}(x) = \sigma^{3}\Phi^{3}(z)\).

Unlike Table D.1 this table carries negative arguments, because a stock level below the mean is an ordinary situation in inventory work and the loss functions have no symmetry to exploit.

Table D.2: The standard normal density, complementary distribution function, and loss functions of orders one through three. Notice that every column is strictly decreasing in \(z\) and that each order falls faster than the one before it, because each is a tail accumulation of its predecessor.

\(z\)	\(\phi(z)\)	\(\Phi^{0}(z)\)	\(\Phi^{1}(z)\)	\(\Phi^{2}(z)\)	\(\Phi^{3}(z)\)
\(-3.0\)	0.0044	0.9987	3.0004	4.9999	6.0000
\(-2.9\)	0.0060	0.9981	2.9005	4.7049	5.5149
\(-2.8\)	0.0079	0.9974	2.8008	4.4198	5.0587
\(-2.7\)	0.0104	0.9965	2.7011	4.1447	4.6306
\(-2.6\)	0.0136	0.9953	2.6015	3.8796	4.2295
\(-2.5\)	0.0175	0.9938	2.5020	3.6244	3.8543
\(-2.4\)	0.0224	0.9918	2.4027	3.3792	3.5042
\(-2.3\)	0.0283	0.9893	2.3037	3.1438	3.1782
\(-2.2\)	0.0355	0.9861	2.2049	2.9184	2.8751
\(-2.1\)	0.0440	0.9821	2.1065	2.7029	2.5942
\(-2.0\)	0.0540	0.9772	2.0085	2.4971	2.3342
\(-1.9\)	0.0656	0.9713	1.9111	2.3011	2.0944
\(-1.8\)	0.0790	0.9641	1.8143	2.1149	1.8737
\(-1.7\)	0.0940	0.9554	1.7183	1.9383	1.6711
\(-1.6\)	0.1109	0.9452	1.6232	1.7712	1.4857
\(-1.5\)	0.1295	0.9332	1.5293	1.6136	1.3166
\(-1.4\)	0.1497	0.9192	1.4367	1.4653	1.1627
\(-1.3\)	0.1714	0.9032	1.3455	1.3262	1.0232
\(-1.2\)	0.1942	0.8849	1.2561	1.1961	0.8972
\(-1.1\)	0.2179	0.8643	1.1686	1.0749	0.7837
\(-1.0\)	0.2420	0.8413	1.0833	0.9623	0.6819
\(-0.9\)	0.2661	0.8159	1.0004	0.8582	0.5909
\(-0.8\)	0.2897	0.7881	0.9202	0.7622	0.5100
\(-0.7\)	0.3123	0.7580	0.8429	0.6740	0.4382
\(-0.6\)	0.3332	0.7257	0.7687	0.5935	0.3749
\(-0.5\)	0.3521	0.6915	0.6978	0.5202	0.3193
\(-0.4\)	0.3683	0.6554	0.6304	0.4538	0.2707
\(-0.3\)	0.3814	0.6179	0.5668	0.3940	0.2283
\(-0.2\)	0.3910	0.5793	0.5069	0.3403	0.1917
\(-0.1\)	0.3970	0.5398	0.4509	0.2925	0.1601
\(0.0\)	0.3989	0.5000	0.3989	0.2500	0.1330
\(0.1\)	0.3970	0.4602	0.3509	0.2125	0.1099
\(0.2\)	0.3910	0.4207	0.3069	0.1797	0.0903
\(0.3\)	0.3814	0.3821	0.2668	0.1510	0.0738
\(0.4\)	0.3683	0.3446	0.2304	0.1262	0.0600
\(0.5\)	0.3521	0.3085	0.1978	0.1048	0.0485
\(0.6\)	0.3332	0.2743	0.1687	0.0865	0.0389
\(0.7\)	0.3123	0.2420	0.1429	0.0710	0.0311
\(0.8\)	0.2897	0.2119	0.1202	0.0578	0.0246
\(0.9\)	0.2661	0.1841	0.1004	0.0468	0.0194
\(1.0\)	0.2420	0.1587	0.0833	0.0377	0.0152
\(1.1\)	0.2179	0.1357	0.0686	0.0301	0.0118
\(1.2\)	0.1942	0.1151	0.0561	0.0239	0.0092
\(1.3\)	0.1714	0.0968	0.0455	0.0188	0.0070
\(1.4\)	0.1497	0.0808	0.0367	0.0147	0.0054
\(1.5\)	0.1295	0.0668	0.0293	0.0114	0.0041
\(1.6\)	0.1109	0.0548	0.0232	0.0088	0.0031
\(1.7\)	0.0940	0.0446	0.0183	0.0067	0.0023
\(1.8\)	0.0790	0.0359	0.0143	0.0051	0.0017
\(1.9\)	0.0656	0.0287	0.0111	0.0039	0.0012
\(2.0\)	0.0540	0.0228	0.0085	0.0029	0.0009
\(2.1\)	0.0440	0.0179	0.0065	0.0021	0.0007
\(2.2\)	0.0355	0.0139	0.0049	0.0016	0.0005
\(2.3\)	0.0283	0.0107	0.0037	0.0012	0.0003
\(2.4\)	0.0224	0.0082	0.0027	0.0008	0.0002
\(2.5\)	0.0175	0.0062	0.0020	0.0006	0.0002
\(2.6\)	0.0136	0.0047	0.0015	0.0004	0.0001
\(2.7\)	0.0104	0.0035	0.0011	0.0003	0.0001
\(2.8\)	0.0079	0.0026	0.0008	0.0002	0.0001
\(2.9\)	0.0060	0.0019	0.0005	0.0001	0.0000
\(3.0\)	0.0044	0.0013	0.0004	0.0001	0.0000
\(3.1\)	0.0033	0.0010	0.0003	0.0001	0.0000
\(3.2\)	0.0024	0.0007	0.0002	0.0000	0.0000
\(3.3\)	0.0017	0.0005	0.0001	0.0000	0.0000
\(3.4\)	0.0012	0.0003	0.0001	0.0000	0.0000
\(3.5\)	0.0009	0.0002	0.0001	0.0000	0.0000
\(3.6\)	0.0006	0.0002	0.0000	0.0000	0.0000
\(3.7\)	0.0004	0.0001	0.0000	0.0000	0.0000
\(3.8\)	0.0003	0.0001	0.0000	0.0000	0.0000
\(3.9\)	0.0002	0.0000	0.0000	0.0000	0.0000
\(4.0\)	0.0001	0.0000	0.0000	0.0000	0.0000

D.3 Cumulative Poisson Probabilities

Table D.3 gives \(G(x) = P\{X \le x\}\) for a Poisson random variable with mean \(\lambda\). Recall from Equation C.9 that the complementary function used throughout the loss function material is \(G^{0}(x) = 1 - G(x) = P\{X > x\}\), which is \(P\{X \ge x+1\}\) and not \(P\{X \ge x\}\). Subtracting a table entry from one gives \(G^{0}\) directly.

For example, the discrete newsvendor rule of Equation 7.13 asks for the smallest \(x\) whose cumulative probability reaches a critical ratio. At \(\lambda = 6\) and a ratio of 0.6628, reading down the \(\lambda = 6\) column gives \(G(6) = 0.6063\), which is short, and \(G(7) = 0.7440\), which clears it.

Table D.3: The Poisson cumulative distribution function \(G(x)\). An entry printed as 1.0000 is not exactly one; it is a probability that rounds to one at four decimal places.

\(x\)	\(0.5\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7.5\)	\(8\)	\(10\)	\(12\)	\(15\)
0	0.6065	0.3679	0.1353	0.0498	0.0183	0.0067	0.0025	0.0006	0.0003	0.0000	0.0000	0.0000
1	0.9098	0.7358	0.4060	0.1991	0.0916	0.0404	0.0174	0.0047	0.0030	0.0005	0.0001	0.0000
2	0.9856	0.9197	0.6767	0.4232	0.2381	0.1247	0.0620	0.0203	0.0138	0.0028	0.0005	0.0000
3	0.9982	0.9810	0.8571	0.6472	0.4335	0.2650	0.1512	0.0591	0.0424	0.0103	0.0023	0.0002
4	0.9998	0.9963	0.9473	0.8153	0.6288	0.4405	0.2851	0.1321	0.0996	0.0293	0.0076	0.0009
5	1.0000	0.9994	0.9834	0.9161	0.7851	0.6160	0.4457	0.2414	0.1912	0.0671	0.0203	0.0028
6	1.0000	0.9999	0.9955	0.9665	0.8893	0.7622	0.6063	0.3782	0.3134	0.1301	0.0458	0.0076
7	1.0000	1.0000	0.9989	0.9881	0.9489	0.8666	0.7440	0.5246	0.4530	0.2202	0.0895	0.0180
8	1.0000	1.0000	0.9998	0.9962	0.9786	0.9319	0.8472	0.6620	0.5925	0.3328	0.1550	0.0374
9	1.0000	1.0000	1.0000	0.9989	0.9919	0.9682	0.9161	0.7764	0.7166	0.4579	0.2424	0.0699
10	1.0000	1.0000	1.0000	0.9997	0.9972	0.9863	0.9574	0.8622	0.8159	0.5830	0.3472	0.1185
11	1.0000	1.0000	1.0000	0.9999	0.9991	0.9945	0.9799	0.9208	0.8881	0.6968	0.4616	0.1848
12	1.0000	1.0000	1.0000	1.0000	0.9997	0.9980	0.9912	0.9573	0.9362	0.7916	0.5760	0.2676
13	1.0000	1.0000	1.0000	1.0000	0.9999	0.9993	0.9964	0.9784	0.9658	0.8645	0.6815	0.3632
14	1.0000	1.0000	1.0000	1.0000	1.0000	0.9998	0.9986	0.9897	0.9827	0.9165	0.7720	0.4657
15	1.0000	1.0000	1.0000	1.0000	1.0000	0.9999	0.9995	0.9954	0.9918	0.9513	0.8444	0.5681
16	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9998	0.9980	0.9963	0.9730	0.8987	0.6641
17	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9999	0.9992	0.9984	0.9857	0.9370	0.7489
18	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9997	0.9993	0.9928	0.9626	0.8195
19	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9999	0.9997	0.9965	0.9787	0.8752
20	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9999	0.9984	0.9884	0.9170
21	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9993	0.9939	0.9469
22	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9997	0.9970	0.9673
23	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9999	0.9985	0.9805
24	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9993	0.9888
25	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9997	0.9938

D.4 Poisson Loss Functions

Chapter 8 works the Poisson case by hand, and doing so needs the loss functions rather than the probabilities. Table D.4 and Table D.5 give them at the same values of \(\lambda\).

Read Table D.4 as the expected number of units of demand that go unmet when \(x\) units are available. Notice that the entry at \(x = 0\) is \(G^{1}(0) = \lambda\), the whole of expected demand, which is the arithmetic check on any column.

Table D.4: The Poisson first order loss function \(G^{1}(x)\), the expected shortage against a stock level of \(x\).

\(x\)	\(0.5\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7.5\)	\(8\)	\(10\)	\(12\)	\(15\)
0	0.5000	1.0000	2.0000	3.0000	4.0000	5.0000	6.0000	7.5000	8.0000	10.0000	12.0000	15.0000
1	0.1065	0.3679	1.1353	2.0498	3.0183	4.0067	5.0025	6.5006	7.0003	9.0000	11.0000	14.0000
2	0.0163	0.1036	0.5413	1.2489	2.1099	3.0472	4.0198	5.5053	6.0034	8.0005	10.0001	13.0000
3	0.0019	0.0233	0.2180	0.6721	1.3480	2.1718	3.0818	4.5255	5.0171	7.0033	9.0006	12.0000
4	0.0002	0.0043	0.0751	0.3194	0.7815	1.4368	2.2330	3.5847	4.0595	6.0137	8.0029	11.0003
5	0.0000	0.0007	0.0225	0.1346	0.4103	0.8773	1.5181	2.7167	3.1591	5.0429	7.0105	10.0011
6	0.0000	0.0001	0.0059	0.0507	0.1954	0.4933	0.9637	1.9582	2.3504	4.1100	6.0308	9.0039
7	0.0000	0.0000	0.0014	0.0172	0.0848	0.2555	0.5700	1.3363	1.6637	3.2401	5.0767	8.0115
8	0.0000	0.0000	0.0003	0.0053	0.0336	0.1221	0.3140	0.8609	1.1167	2.4604	4.1662	7.0295
9	0.0000	0.0000	0.0001	0.0015	0.0123	0.0540	0.1613	0.5229	0.7092	1.7932	3.3212	6.0670
10	0.0000	0.0000	0.0000	0.0004	0.0041	0.0222	0.0773	0.2993	0.4259	1.2511	2.5636	5.1368
11	0.0000	0.0000	0.0000	0.0001	0.0013	0.0085	0.0347	0.1616	0.2417	0.8341	1.9108	4.2553
12	0.0000	0.0000	0.0000	0.0000	0.0004	0.0030	0.0146	0.0823	0.1298	0.5309	1.3724	3.4401
13	0.0000	0.0000	0.0000	0.0000	0.0001	0.0010	0.0058	0.0397	0.0660	0.3225	0.9484	2.7077
14	0.0000	0.0000	0.0000	0.0000	0.0000	0.0003	0.0022	0.0181	0.0318	0.1869	0.6299	2.0709
15	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0008	0.0078	0.0146	0.1035	0.4019	1.5365
16	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0003	0.0032	0.0064	0.0547	0.2464	1.1046
17	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0013	0.0026	0.0277	0.1451	0.7688
18	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0005	0.0010	0.0134	0.0821	0.5176
19	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0002	0.0004	0.0062	0.0447	0.3371
20	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0001	0.0028	0.0234	0.2123
21	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0012	0.0118	0.1293
22	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0005	0.0057	0.0762
23	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0002	0.0027	0.0435
24	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0012	0.0240
25	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0005	0.0128

Table D.5: The Poisson second order loss function \(G^{2}(x)\). The entry at \(x = 0\) is \(\tfrac{1}{2}E[X(X-1)] = \lambda^{2}/2\), which is the check on this table, and the values run in units squared.

\(x\)	\(0.5\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7.5\)	\(8\)	\(10\)	\(12\)	\(15\)
0	0.1250	0.5000	2.0000	4.5000	8.0000	12.5000	18.0000	28.1250	32.0000	50.0000	72.0000	112.5000
1	0.0185	0.1321	0.8647	2.4502	4.9817	8.4933	12.9975	21.6244	24.9997	41.0000	61.0000	98.5000
2	0.0021	0.0285	0.3233	1.2013	2.8718	5.4461	8.9777	16.1192	18.9963	32.9994	50.9999	85.5000
3	0.0002	0.0051	0.1053	0.5292	1.5238	3.2743	5.8959	11.5937	13.9792	25.9961	41.9993	73.4999
4	0.0000	0.0008	0.0302	0.2098	0.7423	1.8374	3.6629	8.0090	9.9197	19.9824	33.9964	62.4997
5	0.0000	0.0001	0.0077	0.0752	0.3320	0.9601	2.1448	5.2923	6.7606	14.9395	26.9859	52.4986
6	0.0000	0.0000	0.0018	0.0245	0.1366	0.4668	1.1811	3.3342	4.4102	10.8296	20.9551	43.4947
7	0.0000	0.0000	0.0004	0.0073	0.0518	0.2113	0.6111	1.9978	2.7465	7.5894	15.8784	35.4831
8	0.0000	0.0000	0.0001	0.0020	0.0182	0.0892	0.2970	1.1369	1.6298	5.1291	11.7122	28.4536
9	0.0000	0.0000	0.0000	0.0005	0.0059	0.0352	0.1358	0.6140	0.9206	3.3359	8.3910	22.3866
10	0.0000	0.0000	0.0000	0.0001	0.0018	0.0130	0.0584	0.3147	0.4947	2.0848	5.8274	17.2498
11	0.0000	0.0000	0.0000	0.0000	0.0005	0.0045	0.0237	0.1531	0.2530	1.2507	3.9166	12.9945
12	0.0000	0.0000	0.0000	0.0000	0.0001	0.0015	0.0091	0.0708	0.1231	0.7197	2.5442	9.5544
13	0.0000	0.0000	0.0000	0.0000	0.0000	0.0005	0.0033	0.0311	0.0571	0.3973	1.5958	6.8468
14	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0011	0.0130	0.0253	0.2103	0.9659	4.7759
15	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0004	0.0052	0.0107	0.1069	0.5640	3.2393
16	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0020	0.0043	0.0521	0.3176	2.1347
17	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0007	0.0017	0.0244	0.1726	1.3659
18	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0003	0.0006	0.0110	0.0905	0.8483
19	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0001	0.0002	0.0048	0.0458	0.5113
20	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0020	0.0224	0.2990
21	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0008	0.0106	0.1696
22	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0003	0.0048	0.0934
23	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0021	0.0499
24	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0009	0.0259
25	0.0000	0.0000	0.0000	-0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0004	0.0131