### **SECTION 110 METHOD OF ESTIMATING PERCENTAGE OF MATERIAL WITHIN SPECIFICATION LIMITS (PWL)**

**110‑01 GENERAL.** When the specifications provide for acceptance of
material based on the method of estimating percentage of material within
specification limits (PWL), the PWL will be determined in accordance
with this section. All test results for a lot will be analyzed
statistically to determine the total estimated percent of the lot that
is within specification limits. The PWL is computed using the sample
average (X) and sample standard deviation (S~n~) of the specified number
(n) of sublots for the lot and the specification tolerance limits, L for
lower and U for upper, for the particular acceptance parameter. From
these values, the respective Quality index(s), Q~L~ for Lower Quality
Index and/or Q~U~ for Upper Quality Index, is computed and the PWL for
the lot for the specified n is determined from Table 1. All
specification limits specified in the technical sections shall be
absolute values. Test results used in the calculations shall be to the
significant figure given in the test procedure.

There is some degree of uncertainty (risk) in the measurement for
acceptance because only a small fraction of production material (the
population) is sampled and tested. This uncertainty exists because all
portions of the production material have the same probability to be
randomly sampled. The Contractor\'s risk is the probability that
material produced at the acceptable quality level is rejected or
subjected to a pay adjustment. The Owner's risk is the probability that
material produced at the rejectable quality level is accepted.

IT IS THE INTENT OF THIS SECTION TO INFORM THE CONTRACTOR THAT, IN ORDER
TO CONSISTENTLY OFFSET THE CONTRACTOR'S RISK FOR MATERIAL EVALUATED,
PRODUCTION QUALITY (USING POPULATION AVERAGE AND POPULATION STANDARD
DEVIATION) MUST BE MAINTAINED AT THE ACCEPTABLE QUALITY SPECIFIED OR
HIGHER. IN ALL CASES, IT IS THE RESPONSIBILITY OF THE CONTRACTOR TO
PRODUCE AT QUALITY LEVELS THAT WILL MEET THE SPECIFIED ACCEPTANCE
CRITERIA WHEN SAMPLED AND TESTED AT THE FREQUENCIES SPECIFIED.

**\* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \*
\* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \*
\* \* \* \* \* \* \* \* \* \* \* \* \* \***

> **Paragraph 110-01 shall be included verbatim in all projects.**

**\* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \*
\* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \* \*
\* \* \* \* \* \* \* \* \* \* \* \* \* \***

**110‑02 METHOD FOR COMPUTING PWL.** The computational sequence for
computing PWL is as follows:

**a.** Divide the lot into n sublots in accordance with the acceptance
requirements of the specification.

**b**. Locate the random sampling position within the sublot in
accordance with the requirements of the specification.

**c.** Make a measurement at each location, or take a test portion and
make the measurement on the test portion in

accordance with the testing requirements of the specification.

**d.** Find the sample average (X) for all sublot values within the lot
by using the following formula:

X = (x~1~ + x~2~ + x~3~ + . . .x~n~) / n

Where: X = Sample average of all sublot values within a lot

x~1~, x~2~ = Individual sublot values

n = Number of sublots

**e.** Find the sample standard deviation (S~n~) by use of the following
formula:

S~n~ = \[(d~1~^2^ + d~2~^2^ + d~3~^2^ + . . .d~n~^2^)/(n‑1)\]^1/2^

Where: S~n~ = Sample standard deviation of the number of sublot values
in the set

d~1~, d~2~, = Deviations of the individual sublot values x~1~, x~2~, ...
from the average value X

that is: d~1~ = (x~1~ ‑ X), d~2~ = (x~2~ ‑ X) ... d~n~ = (x~n~ ‑ X)

n = Number of sublots

**f.** For single sided specification limits (i.e., L only), compute the
Lower Quality Index Q~L~ by use of the following formula:

Q~L~ = (X ‑ L) / S~n~

Where: L = specification lower tolerance limit

Estimate the percentage of material within limits (PWL) by entering
Table 1 with Q~L~, using the column appropriate to the total number (n)
of measurements. If the value of Q~L~ falls between values shown on the
table, use the next higher value of PWL.

**g.** For double-sided specification limits (i.e. L and U), compute the
Quality Indexes Q~L~ and Q~U~ by use of the following formulas:

Q~L~ = (X ‑ L) / Sn and Q~U~ = (U ‑ X) / Sn

Where: L and U = specification lower and upper tolerance limits

Estimate the percentage of material between the lower (L) and upper (U)
tolerance limits (PWL) by entering Table 1 separately with Q~L~ and
Q~U~, using the column appropriate to the total number (n) of
measurements, and determining the percent of material above P~L~ and
percent of material below P~U~ for each tolerance limit. If the values
of Q~L~ fall between values shown on the table, use the next higher
value of P~L~ or P~U~. Determine the PWL by use of the following
formula:

PWL = (P~U~ + P~L~) ‑ 100

Where: P~L~ = percent within lower specification limit

P~U~ = percent within upper specification limit

**EXAMPLE OF PWL CALCULATION**

**Project:** Example Project

**Test Item:** Item P‑401, Lot A.

**A. PWL Determination for Mat Density.**

**1.** Density of four random cores taken from Lot A.

A‑1 96.60

A‑2 97.55

A‑3 99.30

A‑4 98.35

n = 4

**2.** Calculate average density for the lot.

X = (x1 + x2 + x3 + . . .xn) / n

X = (96.60 + 97.55 + 99.30 + 98.35) / 4

X = 97.95 percent density

**3.** Calculate the standard deviation for the lot.

Sn = \[((96.60 ‑ 97.95)^2^ + (97.55 ‑ 97.95)^2^ +(99.30 ‑97.95)^2^ +
(98.35 ‑97.95)^2^)) / (4 ‑ 1)\]^1/2^

Sn = \[(1.82 + 0.16 + 1.82 + 0.16) / 3\]^1/2^

Sn = 1.15

**4.** Calculate the Lower Quality Index Q~L~ for the lot. (L=96.3)

Q~L~ = (X ‑L) / Sn

Q~L~ = (97.95 ‑ 96.30) / 1.15

Q~L~ = 1.4348

**5.** Determine PWL by entering Table 1 with Q~L~= 1.44 and n= 4.

PWL = 98

**B. PWL Determination for Air Voids.**

**1.** Air Voids of four random samples taken from Lot A.

A‑1 5.00

A‑2 3.74

A‑3 2.30

A‑4 3.25

**2.** Calculate the average air voids for the lot.

X = (x1 + x + x3 . . .n) / n

X = (5.00 + 3.74 + 2.30 + 3.25) / 4

X = 3.57 percent

**3.** Calculate the standard deviation Sn for the lot.

Sn = \[((3.57 ‑ 5.00)^2^ + (3.57 ‑ 3.74)^2^ + (3.57 ‑ 2.30)^2^ + (3.57
‑3.25)^2^) / (4 ‑ 1)\]^1/2^

Sn = \[(2.04 + 0.03 + 1.62 + 0.10 ) / 3\]^1/2^

Sn = 1.12

**4.** Calculate the Lower Quality Index Q~L~ for the lot. (L= 2.0)

Q~L~ = (X ‑ L) / Sn

Q~L~ = (3.57 ‑ 2.00) / 1.12

Q~L~ = 1.3992

**5.** Determine P~L~ by entering Table 1 with Q~L~ = 1.41 and n = 4.

PL = 97

**6.** Calculate the Upper Quality Index Q~U~ for the lot. (U= 5.0)

Q~U~ = (U ‑ X) / Sn

Q~U~ = (5.00 ‑ 3.57) / 1.12

Q~U~ = 1.2702

**7.** Determine P~U~ by entering Table 1 with Q~U~ = 1.29 and n = 4.

P~U~ = 93

**8.** Calculate Air Voids PWL

> PWL = (P~L~ + P~U~) ‑ 100
>
> PWL = (97 + 93) ‑ 100 = 90

**EXAMPLE OF OUTLIER CALCULATION (Reference ASTM E 178)**

**Project:** Example Project

**Test Item:** Item P‑401, Lot A.

**A. Outlier Determination for Mat Density.**

**1.** Density of four random cores taken from Lot A. arranged in
descending order.

A‑3 99.30

A‑4 98.35

A‑2 97.55

A‑1 96.60

**2.** Use n=4 and upper 5 percent significance level of to find the
critical value for test criterion = 1.463.

**3.** Use average density, standard deviation, and test criterion value
to evaluate density measurements.

**a.** For measurements greater than the average:

If: (measurement - average)/(standard deviation) is less than test
criterion,

Then: the measurement is not considered an outlier

for A‑3 Check if ( 99.30 - 97.95 ) / 1.15 greater than 1.463

1.174 is less than 1.463, the value is not an outlier

**b.** For measurements less than the average:

If (average - measurement)/(standard deviation) is less than test
criterion,

the measurement is not considered an outlier

for A‑1 Check if ( 97.95 - 96.60 ) / 1.15 greater than 1.463

1.0 is less than 1.463, the value is not an outlier

> NOTE: In this example, a measurement would be considered an outlier if
> the density was:
>
> greater than (97.95+1.463x1.15) = 99.63 percent or,

less than (97.95-1.463x1.15) = 96.27 percent

+--------------+------+------+------+------+------+------+------+------+
| **TABLE 1.   |      |      |      |      |      |      |      |      |
| TABLE FOR    |      |      |      |      |      |      |      |      |
| ESTIMATING   |      |      |      |      |      |      |      |      |
| PERCENT OF   |      |      |      |      |      |      |      |      |
| LOT WITHIN   |      |      |      |      |      |      |      |      |
| LIMITS       |      |      |      |      |      |      |      |      |
| (PWL)**      |      |      |      |      |      |      |      |      |
+--------------+------+------+------+------+------+------+------+------+
| Percent      | Posi |      |      |      |      |      |      |      |
| Within       | tive |      |      |      |      |      |      |      |
| Limits       | Va   |      |      |      |      |      |      |      |
|              | lues |      |      |      |      |      |      |      |
| (P~L~ and    | of Q |      |      |      |      |      |      |      |
| P~U~)        | (    |      |      |      |      |      |      |      |
|              | Q~L~ |      |      |      |      |      |      |      |
|              | and  |      |      |      |      |      |      |      |
|              | Q    |      |      |      |      |      |      |      |
|              | ~U~) |      |      |      |      |      |      |      |
+--------------+------+------+------+------+------+------+------+------+
|              | n=3  | n=4  | n=5  | n=6  | n=7  | n=8  | n=9  | n=10 |
+--------------+------+------+------+------+------+------+------+------+
| 99           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 2.   |
|              | 1541 | 4700 | 6714 | 8008 | 8888 | 9520 | 9994 | 0362 |
+--------------+------+------+------+------+------+------+------+------+
| 98           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1524 | 4400 | 6016 | 6982 | 7612 | 8053 | 8379 | 8630 |
+--------------+------+------+------+------+------+------+------+------+
| 97           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1496 | 4100 | 5427 | 6181 | 6661 | 6993 | 7235 | 7420 |
+--------------+------+------+------+------+------+------+------+------+
| 96           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1456 | 3800 | 4897 | 5497 | 5871 | 6127 | 6313 | 6454 |
+--------------+------+------+------+------+------+------+------+------+
| 95           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1405 | 3500 | 4407 | 4887 | 5181 | 5381 | 5525 | 5635 |
+--------------+------+------+------+------+------+------+------+------+
| 94           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1342 | 3200 | 3946 | 4329 | 4561 | 4717 | 4829 | 4914 |
+--------------+------+------+------+------+------+------+------+------+
| 93           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1269 | 2900 | 3508 | 3810 | 3991 | 4112 | 4199 | 4265 |
+--------------+------+------+------+------+------+------+------+------+
| 92           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1184 | 2600 | 3088 | 3323 | 3461 | 3554 | 3620 | 3670 |
+--------------+------+------+------+------+------+------+------+------+
| 91           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 1089 | 2300 | 2683 | 2860 | 2964 | 3032 | 3081 | 3118 |
+--------------+------+------+------+------+------+------+------+------+
| 90           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 0982 | 2000 | 2290 | 2419 | 2492 | 2541 | 2576 | 2602 |
+--------------+------+------+------+------+------+------+------+------+
| 89           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 0864 | 1700 | 1909 | 1995 | 2043 | 2075 | 2098 | 2115 |
+--------------+------+------+------+------+------+------+------+------+
| 88           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 0736 | 1400 | 1537 | 1587 | 1613 | 1630 | 1643 | 1653 |
+--------------+------+------+------+------+------+------+------+------+
| 87           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 0597 | 1100 | 1173 | 1192 | 1199 | 1204 | 1208 | 1212 |
+--------------+------+------+------+------+------+------+------+------+
| 86           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 0448 | 0800 | 0817 | 0808 | 0800 | 0794 | 0791 | 0789 |
+--------------+------+------+------+------+------+------+------+------+
| 85           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   |
|              | 0288 | 0500 | 0467 | 0435 | 0413 | 0399 | 0389 | 0382 |
+--------------+------+------+------+------+------+------+------+------+
| 84           | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 1.   | 0.   |
|              | 0119 | 0200 | 0124 | 0071 | 0037 | 0015 | 0000 | 9990 |
+--------------+------+------+------+------+------+------+------+------+
| 83           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 9939 | 9900 | 9785 | 9715 | 9671 | 9643 | 9624 | 9610 |
+--------------+------+------+------+------+------+------+------+------+
| 82           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 9749 | 9600 | 9452 | 9367 | 9315 | 9281 | 9258 | 9241 |
+--------------+------+------+------+------+------+------+------+------+
| 81           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 9550 | 9300 | 9123 | 9025 | 8966 | 8928 | 8901 | 8882 |
+--------------+------+------+------+------+------+------+------+------+
| 80           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 9342 | 9000 | 8799 | 8690 | 8625 | 8583 | 8554 | 8533 |
+--------------+------+------+------+------+------+------+------+------+
| 79           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 9124 | 8700 | 8478 | 8360 | 8291 | 8245 | 8214 | 8192 |
+--------------+------+------+------+------+------+------+------+------+
| 78           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 8897 | 8400 | 8160 | 8036 | 7962 | 7915 | 7882 | 7858 |
+--------------+------+------+------+------+------+------+------+------+
| 77           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 8662 | 8100 | 7846 | 7716 | 7640 | 7590 | 7556 | 7531 |
+--------------+------+------+------+------+------+------+------+------+
| 76           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 8417 | 7800 | 7535 | 7401 | 7322 | 7271 | 7236 | 7211 |
+--------------+------+------+------+------+------+------+------+------+
| 75           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 8165 | 7500 | 7226 | 7089 | 7009 | 6958 | 6922 | 6896 |
+--------------+------+------+------+------+------+------+------+------+
| 74           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 7904 | 7200 | 6921 | 6781 | 6701 | 6649 | 6613 | 6587 |
+--------------+------+------+------+------+------+------+------+------+
| 73           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 7636 | 6900 | 6617 | 6477 | 6396 | 6344 | 6308 | 6282 |
+--------------+------+------+------+------+------+------+------+------+
| 72           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 7360 | 6600 | 6316 | 6176 | 6095 | 6044 | 6008 | 5982 |
+--------------+------+------+------+------+------+------+------+------+
| 71           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 7077 | 6300 | 6016 | 5878 | 5798 | 5747 | 5712 | 5686 |
+--------------+------+------+------+------+------+------+------+------+
| 70           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 6787 | 6000 | 5719 | 5582 | 5504 | 5454 | 5419 | 5394 |
+--------------+------+------+------+------+------+------+------+------+
| 69           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 6490 | 5700 | 5423 | 5290 | 5213 | 5164 | 5130 | 5105 |
+--------------+------+------+------+------+------+------+------+------+
| 68           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 6187 | 5400 | 5129 | 4999 | 4924 | 4877 | 4844 | 4820 |
+--------------+------+------+------+------+------+------+------+------+
| 67           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 5878 | 5100 | 4836 | 4710 | 4638 | 4592 | 4560 | 4537 |
+--------------+------+------+------+------+------+------+------+------+
| 66           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 5563 | 4800 | 4545 | 4424 | 4355 | 4310 | 4280 | 4257 |
+--------------+------+------+------+------+------+------+------+------+
| 65           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 5242 | 4500 | 4255 | 4139 | 4073 | 4030 | 4001 | 3980 |
+--------------+------+------+------+------+------+------+------+------+
| 64           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 4916 | 4200 | 3967 | 3856 | 3793 | 3753 | 3725 | 3705 |
+--------------+------+------+------+------+------+------+------+------+
| 63           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 4586 | 3900 | 3679 | 3575 | 3515 | 3477 | 3451 | 3432 |
+--------------+------+------+------+------+------+------+------+------+
| 62           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 4251 | 3600 | 3392 | 3295 | 3239 | 3203 | 3179 | 3161 |
+--------------+------+------+------+------+------+------+------+------+
| 61           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 3911 | 3300 | 3107 | 3016 | 2964 | 2931 | 2908 | 2892 |
+--------------+------+------+------+------+------+------+------+------+
| 60           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 3568 | 3000 | 2822 | 2738 | 2691 | 2660 | 2639 | 2624 |
+--------------+------+------+------+------+------+------+------+------+
| 59           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 3222 | 2700 | 2537 | 2461 | 2418 | 2391 | 2372 | 2358 |
+--------------+------+------+------+------+------+------+------+------+
| 58           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 2872 | 2400 | 2254 | 2186 | 2147 | 2122 | 2105 | 2093 |
+--------------+------+------+------+------+------+------+------+------+
| 57           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 2519 | 2100 | 1971 | 1911 | 1877 | 1855 | 1840 | 1829 |
+--------------+------+------+------+------+------+------+------+------+
| 56           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 2164 | 1800 | 1688 | 1636 | 1607 | 1588 | 1575 | 1566 |
+--------------+------+------+------+------+------+------+------+------+
| 55           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 1806 | 1500 | 1406 | 1363 | 1338 | 1322 | 1312 | 1304 |
+--------------+------+------+------+------+------+------+------+------+
| 54           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 1447 | 1200 | 1125 | 1090 | 1070 | 1057 | 1049 | 1042 |
+--------------+------+------+------+------+------+------+------+------+
| 53           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 1087 | 0900 | 0843 | 0817 | 0802 | 0793 | 0786 | 0781 |
+--------------+------+------+------+------+------+------+------+------+
| 52           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 0725 | 0600 | 0562 | 0544 | 0534 | 0528 | 0524 | 0521 |
+--------------+------+------+------+------+------+------+------+------+
| 51           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 0363 | 0300 | 0281 | 0272 | 0267 | 0264 | 0262 | 0260 |
+--------------+------+------+------+------+------+------+------+------+
| 50           | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   | 0.   |
|              | 0000 | 0000 | 0000 | 0000 | 0000 | 0000 | 0000 | 0000 |
+--------------+------+------+------+------+------+------+------+------+
| **TABLE 1.   |      |      |      |      |      |      |      |      |
| TABLE FOR    |      |      |      |      |      |      |      |      |
| ESTIMATING   |      |      |      |      |      |      |      |      |
| PERCENT OF   |      |      |      |      |      |      |      |      |
| LOT WITHIN   |      |      |      |      |      |      |      |      |
| LIMITS       |      |      |      |      |      |      |      |      |
| (PWL)**      |      |      |      |      |      |      |      |      |
+--------------+------+------+------+------+------+------+------+------+
| Percent      | Nega |      |      |      |      |      |      |      |
| Within       | tive |      |      |      |      |      |      |      |
| Limits       | Va   |      |      |      |      |      |      |      |
|              | lues |      |      |      |      |      |      |      |
| (P~L~ and    | of Q |      |      |      |      |      |      |      |
| P~U~)        | (    |      |      |      |      |      |      |      |
|              | Q~L~ |      |      |      |      |      |      |      |
|              | and  |      |      |      |      |      |      |      |
|              | Q    |      |      |      |      |      |      |      |
|              | ~U~) |      |      |      |      |      |      |      |
+--------------+------+------+------+------+------+------+------+------+
|              | n=3  | n=4  | n=5  | n=6  | n=7  | n=8  | n=9  | n=10 |
+--------------+------+------+------+------+------+------+------+------+
| 49           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 0363 | 0300 | 0281 | 0272 | 0267 | 0264 | 0262 | 0260 |
+--------------+------+------+------+------+------+------+------+------+
| 48           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 0725 | 0600 | 0562 | 0544 | 0534 | 0528 | 0524 | 0521 |
+--------------+------+------+------+------+------+------+------+------+
| 47           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 1087 | 0900 | 0843 | 0817 | 0802 | 0793 | 0786 | 0781 |
+--------------+------+------+------+------+------+------+------+------+
| 46           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 1447 | 1200 | 1125 | 1090 | 1070 | 1057 | 1049 | 1042 |
+--------------+------+------+------+------+------+------+------+------+
| 45           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 1806 | 1500 | 1406 | 1363 | 1338 | 1322 | 1312 | 1304 |
+--------------+------+------+------+------+------+------+------+------+
| 44           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 2164 | 1800 | 1688 | 1636 | 1607 | 1588 | 1575 | 1566 |
+--------------+------+------+------+------+------+------+------+------+
| 43           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 2519 | 2100 | 1971 | 1911 | 1877 | 1855 | 1840 | 1829 |
+--------------+------+------+------+------+------+------+------+------+
| 42           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 2872 | 2400 | 2254 | 2186 | 2147 | 2122 | 2105 | 2093 |
+--------------+------+------+------+------+------+------+------+------+
| 41           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 3222 | 2700 | 2537 | 2461 | 2418 | 2391 | 2372 | 2358 |
+--------------+------+------+------+------+------+------+------+------+
| 40           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 3568 | 3000 | 2822 | 2738 | 2691 | 2660 | 2639 | 2624 |
+--------------+------+------+------+------+------+------+------+------+
| 39           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 3911 | 3300 | 3107 | 3016 | 2964 | 2931 | 2908 | 2892 |
+--------------+------+------+------+------+------+------+------+------+
| 38           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 4251 | 3600 | 3392 | 3295 | 3239 | 3203 | 3179 | 3161 |
+--------------+------+------+------+------+------+------+------+------+
| 37           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 4586 | 3900 | 3679 | 3575 | 3515 | 3477 | 3451 | 3432 |
+--------------+------+------+------+------+------+------+------+------+
| 36           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 4916 | 4200 | 3967 | 3856 | 3793 | 3753 | 3725 | 3705 |
+--------------+------+------+------+------+------+------+------+------+
| 35           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 5242 | 4500 | 4255 | 4139 | 4073 | 4030 | 4001 | 3980 |
+--------------+------+------+------+------+------+------+------+------+
| 34           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 5563 | 4800 | 4545 | 4424 | 4355 | 4310 | 4280 | 4257 |
+--------------+------+------+------+------+------+------+------+------+
| 33           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 5878 | 5100 | 4836 | 4710 | 4638 | 4592 | 4560 | 4537 |
+--------------+------+------+------+------+------+------+------+------+
| 32           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 6187 | 5400 | 5129 | 4999 | 4924 | 4877 | 4844 | 4820 |
+--------------+------+------+------+------+------+------+------+------+
| 31           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 6490 | 5700 | 5423 | 5290 | 5213 | 5164 | 5130 | 5105 |
+--------------+------+------+------+------+------+------+------+------+
| 30           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 6787 | 6000 | 5719 | 5582 | 5504 | 5454 | 5419 | 5394 |
+--------------+------+------+------+------+------+------+------+------+
| 29           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 7077 | 6300 | 6016 | 5878 | 5798 | 5747 | 5712 | 5686 |
+--------------+------+------+------+------+------+------+------+------+
| 28           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 7360 | 6600 | 6316 | 6176 | 6095 | 6044 | 6008 | 5982 |
+--------------+------+------+------+------+------+------+------+------+
| 27           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 7636 | 6900 | 6617 | 6477 | 6396 | 6344 | 6308 | 6282 |
+--------------+------+------+------+------+------+------+------+------+
| 26           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 7904 | 7200 | 6921 | 6781 | 6701 | 6649 | 6613 | 6587 |
+--------------+------+------+------+------+------+------+------+------+
| 25           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 8165 | 7500 | 7226 | 7089 | 7009 | 6958 | 6922 | 6896 |
+--------------+------+------+------+------+------+------+------+------+
| 24           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 8417 | 7800 | 7535 | 7401 | 7322 | 7271 | 7236 | 7211 |
+--------------+------+------+------+------+------+------+------+------+
| 23           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 8662 | 8100 | 7846 | 7716 | 7640 | 7590 | 7556 | 7531 |
+--------------+------+------+------+------+------+------+------+------+
| 22           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 8897 | 8400 | 8160 | 8036 | 7962 | 7915 | 7882 | 7858 |
+--------------+------+------+------+------+------+------+------+------+
| 21           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 9124 | 8700 | 8478 | 8360 | 8291 | 8245 | 8214 | 8192 |
+--------------+------+------+------+------+------+------+------+------+
| 20           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 9342 | 9000 | 8799 | 8690 | 8625 | 8583 | 8554 | 8533 |
+--------------+------+------+------+------+------+------+------+------+
| 19           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 9550 | 9300 | 9123 | 9025 | 8966 | 8928 | 8901 | 8882 |
+--------------+------+------+------+------+------+------+------+------+
| 18           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 9749 | 9600 | 9452 | 9367 | 9315 | 9281 | 9258 | 9241 |
+--------------+------+------+------+------+------+------+------+------+
| 17           | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  | -0.  |
|              | 9939 | 9900 | 9785 | 9715 | 9671 | 9643 | 9624 | 9610 |
+--------------+------+------+------+------+------+------+------+------+
| 16           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -0.  |
|              | 0119 | 0200 | 0124 | 0071 | 0037 | 0015 | 0000 | 9990 |
+--------------+------+------+------+------+------+------+------+------+
| 15           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 0288 | 0500 | 0467 | 0435 | 0413 | 0399 | 0389 | 0382 |
+--------------+------+------+------+------+------+------+------+------+
| 14           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 0448 | 0800 | 0817 | 0808 | 0800 | 0794 | 0791 | 0789 |
+--------------+------+------+------+------+------+------+------+------+
| 13           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 0597 | 1100 | 1173 | 1192 | 1199 | 1204 | 1208 | 1212 |
+--------------+------+------+------+------+------+------+------+------+
| 12           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 0736 | 1400 | 1537 | 1587 | 1613 | 1630 | 1643 | 1653 |
+--------------+------+------+------+------+------+------+------+------+
| 11           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 0864 | 1700 | 1909 | 1995 | 2043 | 2075 | 2098 | 2115 |
+--------------+------+------+------+------+------+------+------+------+
| 10           | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 0982 | 2000 | 2290 | 2419 | 2492 | 2541 | 2576 | 2602 |
+--------------+------+------+------+------+------+------+------+------+
| 9            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1089 | 2300 | 2683 | 2860 | 2964 | 3032 | 3081 | 3118 |
+--------------+------+------+------+------+------+------+------+------+
| 8            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1184 | 2600 | 3088 | 3323 | 3461 | 3554 | 3620 | 3670 |
+--------------+------+------+------+------+------+------+------+------+
| 7            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1269 | 2900 | 3508 | 3810 | 3991 | 4112 | 4199 | 4265 |
+--------------+------+------+------+------+------+------+------+------+
| 6            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1342 | 3200 | 3946 | 4329 | 4561 | 4717 | 4829 | 4914 |
+--------------+------+------+------+------+------+------+------+------+
| 5            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1405 | 3500 | 4407 | 4887 | 5181 | 5381 | 5525 | 5635 |
+--------------+------+------+------+------+------+------+------+------+
| 4            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1456 | 3800 | 4897 | 5497 | 5871 | 6127 | 6313 | 6454 |
+--------------+------+------+------+------+------+------+------+------+
| 3            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1496 | 4100 | 5427 | 6181 | 6661 | 6993 | 7235 | 7420 |
+--------------+------+------+------+------+------+------+------+------+
| 2            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  |
|              | 1524 | 4400 | 6016 | 6982 | 7612 | 8053 | 8379 | 8630 |
+--------------+------+------+------+------+------+------+------+------+
| 1            | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -1.  | -2.  |
|              | 1541 | 4700 | 6714 | 8008 | 8888 | 9520 | 9994 | 0362 |
+--------------+------+------+------+------+------+------+------+------+

**END OF SECTION 110**