AP 2006 Statistics FRQ 5 Ap06 51653

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AP® Statistics
2006 Free-Response Questions

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2006 AP® STATISTICS FREE-RESPONSE QUESTIONS

Formulas begin on page 3.
Questions begin on page 6.
Tables begin on page 12.

2

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS

Formulas

(I)

Descriptive Statistics

∑ xi
n

x =

d

i

sx =

2
1
∑ xi − x
n−1

sp =

dn1 − 1is21 + dn2 − 1is22
dn1 − 1i + dn2 − 1i

y = b0 + b1 x

d

id

∑ xi − x yi − y

b1 =

d

∑ xi − x

i

i2

b0 = y − b1 x

r =

b1 = r

sb =
1

FG
H

x − x
1
∑ i
sx
n−1

IJ FG yi − y IJ
K H sy K

sy
sx

d

i2

d

i2

∑ yi − y i
n−2
∑ xi − x

3

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
(II)

Probability

P( A ∪ B ) = P( A) + P( B ) − P( A ∩ B )
P( A B ) =

P( A ∩ B )
P( B )

E ( X ) = µ x = ∑ xi pi

d

Var( X ) = s 2x = ∑ xi − µ x

i2 pi

If X has a binomial distribution with parameters n and p, then:

P( X = k ) =

FG nIJ p k (1 − p)n − k
H kK

µ x = np
sx =

np(1 − p)

µ = p
p
p(1 − p)
n

s =
p

If x is the mean of a random sample of size n from an infinite
population with mean µ and standard deviation s, then:

µx = µ
sx =

s
n

4

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
(III)

Inferential Statistics

Standardized test statistic:

statistic - parameter
standard deviation of statistic

Confidence interval: statistic ± (critical value) ∑ (standard deviation of statistic)
Single-Sample
Standard Deviation
of Statistic

Statistic

σ

Sample Mean

n
p(1 − p)
n

Sample Proportion

Two-Sample
Standard Deviation
of Statistic

Statistic
Difference of
sample means

σ 12
n1

+

σ 22
n2

Special case when σ 1 = σ 2

σ

1
1
+
n1 n2

p1 (1 − p1 )
p (1 − p2 )
+ 2
n1
n2

Difference of
sample proportions

Special case when p1 = p2

b g

p 1− p

Chi-square test statistic =

1
1
+
n1 n2

aobserved − expectedf
∑
expected

5

2

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
STATISTICS
SECTION II
Part A
Questions 1-5
Spend about 65 minutes on this part of the exam.
Percent of Section II grade— 75
Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the
correctness of your methods as well as on the accuracy and completeness of your results and explanations.
1. Two parents have each built a toy catapult for use in a game at an elementary school fair. To play the game,
students will attempt to launch Ping-Pong balls from the catapults so that the balls land within a 5-centimeter
band. A target line will be drawn through the middle of the band, as shown in the figure below. All points on the
target line are equidistant from the launching location.

If a ball lands within the shaded band, the student will win a prize.
The parents have constructed the two catapults according to slightly different plans. They want to test these
catapults before building additional ones. Under identical conditions, the parents launch 40 Ping-Pong balls from
each catapult and measure the distance that the ball travels before landing. Distances to the nearest centimeter
are graphed in the dotplots below.

(a) Comment on any similarities and any differences in the two distributions of distances traveled by balls
launched from catapult A and catapult B.
(b) If the parents want to maximize the probability of having the Ping-Pong balls land within the band, which
one of the two catapults, A or B, would be better to use than the other? Justify your choice.
(c) Using the catapult that you chose in part (b), how many centimeters from the target line should this catapult
be placed? Explain why you chose this distance.
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2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
2. A manufacturer of dish detergent believes the height of soapsuds in the dishpan depends on the amount of
detergent used. A study of the suds’ heights for a new dish detergent was conducted. Seven pans of water were
prepared. All pans were of the same size and type and contained the same amount of water. The temperature of
the water was the same for each pan. An amount of dish detergent was assigned at random to each pan, and that
amount of detergent was added to the pan. Then the water in the dishpan was agitated for a set amount of time,
and the height of the resulting suds was measured.
A plot of the data and the computer output from fitting a least squares regression line to the data are shown
below.

(a) Write the equation of the fitted regression line. Define any variables used in this equation.
(b) Note that s = 1.99821 in the computer output. Interpret this value in the context of this study.
(c) Identify and interpret the standard error of the slope.

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2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
3. The depth from the surface of Earth to a refracting layer beneath the surface can be estimated using methods
developed by seismologists. One method is based on the time required for vibrations to travel from a distant
explosion to a receiving point. The depth measurement (M) is the sum of the true depth (D) and the random
measurement error (E). That is, M = D + E. The measurement error (E) is assumed to be normally distributed
with mean 0 feet and standard deviation 1.5 feet.

(a) If the true depth at a certain point is 2 feet, what is the probability that the depth measurement will be
negative?
(b) Suppose three independent depth measurements are taken at the point where the true depth is 2 feet. What is
the probability that at least one of these measurements will be negative?
(c) What is the probability that the mean of the three independent depth measurements taken at the point where
the true depth is 2 feet will be negative?

4. Patients with heart-attack symptoms arrive at an emergency room either by ambulance or self-transportation
provided by themselves, family, or friends. When a patient arrives at the emergency room, the time of arrival is
recorded. The time when the patient’s diagnostic treatment begins is also recorded.
An administrator of a large hospital wanted to determine whether the mean wait time (time between arrival and
diagnostic treatment) for patients with heart-attack symptoms differs according to the mode of transportation.
A random sample of 150 patients with heart-attack symptoms who had reported to the emergency room was
selected. For each patient, the mode of transportation and wait time were recorded. Summary statistics for each
mode of transportation are shown in the table below.

Mode of
Transportation

Sample Size

Mean Wait Time
(in minutes)

Ambulance
Self

77
73

6.04
8.30

Standard Deviation
of Wait Times
(in minutes)
4.30
5.16

(a) Use a 99 percent confidence interval to estimate the difference between the mean wait times for ambulancetransported patients and self-transported patients at this emergency room.
(b) Based only on this confidence interval, do you think the difference in the mean wait times is statistically
significant? Justify your answer.

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2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
5. A biologist is interested in studying the effect of growth-enhancing nutrients and different salinity (salt) levels in
water on the growth of shrimps. The biologist has ordered a large shipment of young tiger shrimps from a supply
house for use in the study. The experiment is to be conducted in a laboratory where 10 tiger shrimps are placed
randomly into each of 12 similar tanks in a controlled environment. The biologist is planning to use 3 different
growth-enhancing nutrients (A, B, and C) and two different salinity levels (low and high).
(a) List the treatments that the biologist plans to use in this experiment.
(b) Using the treatments listed in part (a), describe a completely randomized design that will allow the biologist
to compare the shrimps’ growth after 3 weeks.
(c) Give one statistical advantage to having only tiger shrimps in the experiment. Explain why this is an
advantage.
(d) Give one statistical disadvantage to having only tiger shrimps in the experiment. Explain why this is a
disadvantage.

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2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
STATISTICS
SECTION II
Part B
Question 6
Spend about 25 minutes on this part of the exam.
Percent of Section II grade— 25
Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the
correctness of your methods as well as on the accuracy and completeness of your results and explanations.
6. A manufacturer of thermostats is concerned that the readings of its thermostats have become less reliable (more
variable). In the past, the variance has been 1.52 degrees Fahrenheit (F) squared. A random sample of 10
recently manufactured thermostats was selected and placed in a room that was maintained at 68°F. The readings
for those 10 thermostats are given in the table below.
Thermostat
Temperature (°F)

1
2
3
4
5
6
7
8
9
10
66.8 67.8 70.6 69.3 65.9 66.2 68.1 68.6 67.9 67.2

(a) State the null and alternative hypotheses that the manufacturer is interested in testing.
It can be shown that if the population of thermostat temperatures is normally distributed, the sampling
distribution of

(n - 1) s 2
s2

(b) Calculate the value of

follows a chi-square distribution with n - 1 degrees of freedom.

(n - 1) s 2
1.52

for these data.

(c) Assume that the population of thermostat temperatures follows a normal distribution. Use the test statistic
(n - 1) s 2
from part (b) and the chi-square distribution to test the hypotheses in part (a).
1.52
(d) For the test conducted in part (c), what is the smallest value of the test statistic that would have led to the
rejection of the null hypothesis at the 5 percent significance level?
Mark this value of the test statistic on the graph of the chi-square distribution below. Indicate the region that
contains all of the values that would have led to the rejection of the null hypothesis.

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2006 AP® STATISTICS FREE-RESPONSE QUESTIONS
(e) Using simulation, 1,000 samples, each of size 10, were randomly generated from 3 populations with
different variances. Each population was normally distributed with mean 68 and variance greater than 1.52.
(n - 1) s 2
for each population.
The histograms below show the simulated sampling distribution of
1.52
Mark the region identified in part (d) on each of the histograms below.

(f) Based on the regions that you marked in part (e), identify the simulated sampling distribution that
corresponds to the population with the largest variance. Then identify the simulated sampling distribution
that corresponds to the population with the smallest variance. Justify your choices.

STOP
END OF EXAM

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11

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS

Probability

Table entry for z is the
probability lying below z.

z
Table A

Standard normal probabilities

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

– 3.4
– 3.3
– 3.2
– 3.1
– 3.0
– 2.9
– 2.8
– 2.7
– 2.6
– 2.5
– 2.4
– 2.3
– 2.2
– 2.1
– 2.0
– 1.9
– 1.8
– 1.7
– 1.6
– 1.5
– 1.4
– 1.3
– 1.2
– 1.1
– 1.0
– 0.9
– 0.8
– 0.7
– 0.6
– 0.5
– 0.4
– 0.3
– 0.2
– 0.1
– 0.0

.0003
.0005
.0007
.0010
.0013
.0019
.0026
.0035
.0047
.0062
.0082
.0107
.0139
.0179
.0228
.0287
.0359
.0446
.0548
.0668
.0808
.0968
.1151
.1357
.1587
.1841
.2119
.2420
.2743
.3085
.3446
.3821
.4207
.4602
.5000

.0003
.0005
.0007
.0009
.0013
.0018
.0025
.0034
.0045
.0060
.0080
.0104
.0136
.0174
.0222
.0281
.0351
.0436
.0537
.0655
.0793
.0951
.1131
.1335
.1562
.1814
.2090
.2389
.2709
.3050
.3409
.3783
.4168
.4562
.4960

.0003
.0005
.0006
.0009
.0013
.0018
.0024
.0033
.0044
.0059
.0078
.0102
.0132
.0170
.0217
.0274
.0344
.0427
.0526
.0643
.0778
.0934
.1112
.1314
.1539
.1788
.2061
.2358
.2676
.3015
.3372
.3745
.4129
.4522
.4920

.0003
.0004
.0006
.0009
.0012
.0017
.0023
.0032
.0043
.0057
.0075
.0099
.0129
.0166
.0212
.0268
.0336
.0418
.0516
.0630
.0764
.0918
.1093
.1292
.1515
.1762
.2033
.2327
.2643
.2981
.3336
.3707
.4090
.4483
.4880

.0003
.0004
.0006
.0008
.0012
.0016
.0023
.0031
.0041
.0055
.0073
.0096
.0125
.0162
.0207
.0262
.0329
.0409
.0505
.0618
.0749
.0901
.1075
.1271
.1492
.1736
.2005
.2296
.2611
.2946
.3300
.3669
.4052
.4443
.4840

.0003
.0004
.0006
.0008
.0011
.0016
.0022
.0030
.0040
.0054
.0071
.0094
.0122
.0158
.0202
.0256
.0322
.0401
.0495
.0606
.0735
.0885
.1056
.1251
.1469
.1711
.1977
.2266
.2578
.2912
.3264
.3632
.4013
.4404
.4801

.0003
.0004
.0006
.0008
.0011
.0015
.0021
.0029
.0039
.0052
.0069
.0091
.0119
.0154
.0197
.0250
.0314
.0392
.0485
.0594
.0721
.0869
.1038
.1230
.1446
.1685
.1949
.2236
.2546
.2877
.3228
.3594
.3974
.4364
.4761

.0003
.0004
.0005
.0008
.0011
.0015
.0021
.0028
.0038
.0051
.0068
.0089
.0116
.0150
.0192
.0244
.0307
.0384
.0475
.0582
.0708
.0853
.1020
.1210
.1423
.1660
.1922
.2206
.2514
.2843
.3192
.3557
.3936
.4325
.4721

.0003
.0004
.0005
.0007
.0010
.0014
.0020
.0027
.0037
.0049
.0066
.0087
.0113
.0146
.0188
.0239
.0301
.0375
.0465
.0571
.0694
.0838
.1003
.1190
.1401
.1635
.1894
.2177
.2483
.2810
.3156
.3520
.3897
.4286
.4681

.0002
.0003
.0005
.0007
.0010
.0014
.0019
.0026
.0036
.0048
.0064
.0084
.0110
.0143
.0183
.0233
.0294
.0367
.0455
.0559
.0681
.0823
.0985
.1170
.1379
.1611
.1867
.2148
.2451
.2776
.3121
.3483
.3859
.4247
.4641

12

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS

Probability

Table entry for z is the
probability lying below z.

z
Table A

(Continued)

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4

.5000
.5398
.5793
.6179
.6554
.6915
.7257
.7580
.7881
.8159
.8413
.8643
.8849
.9032
.9192
.9332
.9452
.9554
.9641
.9713
.9772
.9821
.9861
.9893
.9918
.9938
.9953
.9965
.9974
.9981
.9987
.9990
.9993
.9995
.9997

.5040
.5438
.5832
.6217
.6591
.6950
.7291
.7611
.7910
.8186
.8438
.8665
.8869
.9049
.9207
.9345
.9463
.9564
.9649
.9719
.9778
.9826
.9864
.9896
.9920
.9940
.9955
.9966
.9975
.9982
.9987
.9991
.9993
.9995
.9997

.5080
.5478
.5871
.6255
.6628
.6985
.7324
.7642
.7939
.8212
.8461
.8686
.8888
.9066
.9222
.9357
.9474
.9573
.9656
.9726
.9783
.9830
.9868
.9898
.9922
.9941
.9956
.9967
.9976
.9982
.9987
.9991
.9994
.9995
.9997

.5120
.5517
.5910
.6293
.6664
.7019
.7357
.7673
.7967
.8238
.8485
.8708
.8907
.9082
.9236
.9370
.9484
.9582
.9664
.9732
.9788
.9834
.9871
.9901
.9925
.9943
.9957
.9968
.9977
.9983
.9988
.9991
.9994
.9996
.9997

.5160
.5557
.5948
.6331
.6700
.7054
.7389
.7704
.7995
.8264
.8508
.8729
.8925
.9099
.9251
.9382
.9495
.9591
.9671
.9738
.9793
.9838
.9875
.9904
.9927
.9945
.9959
.9969
.9977
.9984
.9988
.9992
.9994
.9996
.9997

.5199
.5596
.5987
.6368
.6736
.7088
.7422
.7734
.8023
.8289
.8531
.8749
.8944
.9115
.9265
.9394
.9505
.9599
.9678
.9744
.9798
.9842
.9878
.9906
.9929
.9946
.9960
.9970
.9978
.9984
.9989
.9992
.9994
.9996
.9997

.5239
.5636
.6026
.6406
.6772
.7123
.7454
.7764
.8051
.8315
.8554
.8770
.8962
.9131
.9279
.9406
.9515
.9608
.9686
.9750
.9803
.9846
.9881
.9909
.9931
.9948
.9961
.9971
.9979
.9985
.9989
.9992
.9994
.9996
.9997

.5279
.5675
.6064
.6443
.6808
.7157
.7486
.7794
.8078
.8340
.8577
.8790
.8980
.9147
.9292
.9418
.9525
.9616
.9693
.9756
.9808
.9850
.9884
.9911
.9932
.9949
.9962
.9972
.9979
.9985
.9989
.9992
.9995
.9996
.9997

.5319
.5714
.6103
.6480
.6844
.7190
.7517
.7823
.8106
.8365
.8599
.8810
.8997
.9162
.9306
.9429
.9535
.9625
.9699
.9761
.9812
.9854
.9887
.9913
.9934
.9951
.9963
.9973
.9980
.9986
.9990
.9993
.9995
.9996
.9997

.5359
.5753
.6141
.6517
.6879
.7224
.7549
.7852
.8133
.8389
.8621
.8830
.9015
.9177
.9319
.9441
.9545
.9633
.9706
.9767
.9817
.9857
.9890
.9916
.9936
.9952
.9964
.9974
.9981
.9986
.9990
.9993
.9995
.9997
.9998

13

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS

Table entry for p and
C is the point t* with
probability p lying
above it and
probability C lying
between −t * and t*.

Probability p

t*
Table B

t distribution critical values
Tail probability p

df

.25

.20

.15

.10

.05

.025

.02

.01

.005

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
80
100
1000
⬁

1.000
.816
.765
.741
.727
.718
.711
.706
.703
.700
.697
.695
.694
.692
.691
.690
.689
.688
.688
.687
.686
.686
.685
.685
.684
.684
.684
.683
.683
.683
.681
.679
.679
.678
.677
.675
.674

1.376
1.061
.978
.941
.920
.906
.896
.889
.883
.879
.876
.873
.870
.868
.866
.865
.863
.862
.861
.860
.859
.858
.858
.857
.856
.856
.855
.855
.854
.854
.851
.849
.848
.846
.845
.842
.841

1.963
1.386
1.250
1.190
1.156
1.134
1.119
1.108
1.100
1.093
1.088
1.083
1.079
1.076
1.074
1.071
1.069
1.067
1.066
1.064
1.063
1.061
1.060
1.059
1.058
1.058
1.057
1.056
1.055
1.055
1.050
1.047
1.045
1.043
1.042
1.037
1.036

3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.303
1.299
1.296
1.292
1.290
1.282
1.282

6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.676
1.671
1.664
1.660
1.646
1.645

12.71
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.021
2.009
2.000
1.990
1.984
1.962
1.960

15.89
4.849
3.482
2.999
2.757
2.612
2.517
2.449
2.398
2.359
2.328
2.303
2.282
2.264
2.249
2.235
2.224
2.214
2.205
2.197
2.189
2.183
2.177
2.172
2.167
2.162
2.158
2.154
2.150
2.147
2.123
2.109
2.099
2.088
2.081
2.056
2.054

31.82
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.403
2.390
2.374
2.364
2.330
2.326

63.66
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.704
2.678
2.660
2.639
2.626
2.581
2.576

127.3
14.09
7.453
5.598
4.773
4.317
4.029
3.833
3.690
3.581
3.497
3.428
3.372
3.326
3.286
3.252
3.222
3.197
3.174
3.153
3.135
3.119
3.104
3.091
3.078
3.067
3.057
3.047
3.038
3.030
2.971
2.937
2.915
2.887
2.871
2.813
2.807

318.3
22.33
10.21
7.173
5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
3.686
3.646
3.611
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.307
3.261
3.232
3.195
3.174
3.098
3.091

636.6
31.60
12.92
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
3.883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.690
3.674
3.659
3.646
3.551
3.496
3.460
3.416
3.390
3.300
3.291

50%

60%

70%

80%

90%

95%

96%

98%

99%

99.5%

99.8%

99.9%

Confidence level C

14

.0025

.001

.0005

2006 AP® STATISTICS FREE-RESPONSE QUESTIONS

Probability p
Table entry for p is the point
( χ 2 ) with probability p lying
above it.

(χ2 )
Table C

χ 2 critical values
Tail probability p

df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
80
100

.25
1.32
2.77
4.11
5.39
6.63
7.84
9.04
10.22
11.39
12.55
13.70
14.85
15.98
17.12
18.25
19.37
20.49
21.60
22.72
23.83
24.93
26.04
27.14
28.24
29.34
30.43
31.53
32.62
33.71
34.80
45.62
56.33
66.98
88.13
109.1

.20
1.64
3.22
4.64
5.99
7.29
8.56
9.80
11.03
12.24
13.44
14.63
15.81
16.98
18.15
19.31
20.47
21.61
22.76
23.90
25.04
26.17
27.30
28.43
29.55
30.68
31.79
32.91
34.03
35.14
36.25
47.27
58.16
68.97
90.41
111.7

.15

.10

2.07
3.79
5.32
6.74
8.12
9.45
10.75
12.03
13.29
14.53
15.77
16.99
18.20
19.41
20.60
21.79
22.98
24.16
25.33
26.50
27.66
28.82
29.98
31.13
32.28
33.43
34.57
35.71
36.85
37.99
49.24
60.35
71.34
93.11
114.7

2.71
4.61
6.25
7.78
9.24
10.64
12.02
13.36
14.68
15.99
17.28
18.55
19.81
21.06
22.31
23.54
24.77
25.99
27.20
28.41
29.62
30.81
32.01
33.20
34.38
35.56
36.74
37.92
39.09
40.26
51.81
63.17
74.40
96.58
118.5

.05
3.84
5.99
7.81
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
21.03
22.36
23.68
25.00
26.30
27.59
28.87
30.14
31.41
32.67
33.92
35.17
36.42
37.65
38.89
40.11
41.34
42.56
43.77
55.76
67.50
79.08
101.9
124.3

.025
5.02
7.38
9.35
11.14
12.83
14.45
16.01
17.53
19.02
20.48
21.92
23.34
24.74
26.12
27.49
28.85
30.19
31.53
32.85
34.17
35.48
36.78
38.08
39.36
40.65
41.92
43.19
44.46
45.72
46.98
59.34
71.42
83.30
106.6
129.6

15

.02

.01

.005

5.41
7.82
9.84
11.67
13.39
15.03
16.62
18.17
19.68
21.16
22.62
24.05
25.47
26.87
28.26
29.63
31.00
32.35
33.69
35.02
36.34
37.66
38.97
40.27
41.57
42.86
44.14
45.42
46.69
47.96
60.44
72.61
84.58
108.1
131.1

6.63
9.21
11.34
13.28
15.09
16.81
18.48
20.09
21.67
23.21
24.72
26.22
27.69
29.14
30.58
32.00
33.41
34.81
36.19
37.57
38.93
40.29
41.64
42.98
44.31
45.64
46.96
48.28
49.59
50.89
63.69
76.15
88.38
112.3
135.8

7.88
10.60
12.84
14.86
16.75
18.55
20.28
21.95
23.59
25.19
26.76
28.30
29.82
31.32
32.80
34.27
35.72
37.16
38.58
40.00
41.40
42.80
44.18
45.56
46.93
48.29
49.64
50.99
52.34
53.67
66.77
79.49
91.95
116.3
140.2

.0025
9.14
11.98
14.32
16.42
18.39
20.25
22.04
23.77
25.46
27.11
28.73
30.32
31.88
33.43
34.95
36.46
37.95
39.42
40.88
42.34
43.78
45.20
46.62
48.03
49.44
50.83
52.22
53.59
54.97
56.33
69.70
82.66
95.34
120.1
144.3

.001

.0005

10.83
13.82
16.27
18.47
20.51
22.46
24.32
26.12
27.88
29.59
31.26
32.91
34.53
36.12
37.70
39.25
40.79
42.31
43.82
45.31
46.80
48.27
49.73
51.18
52.62
54.05
55.48
56.89
58.30
59.70
73.40
86.66
99.61
124.8
149.4

12.12
15.20
17.73
20.00
22.11
24.10
26.02
27.87
29.67
31.42
33.14
34.82
36.48
38.11
39.72
41.31
42.88
44.43
45.97
47.50
49.01
50.51
52.00
53.48
54.95
56.41
57.86
59.30
60.73
62.16
76.09
89.56
102.7
128.3
153.2



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