Department of Statistics
STAV102
Business Statistics
SICK TEST
Date: 26 October 2024
Time: 120 min
Examiner: Dr L Kepe, Ms S Alexander and Dr S Mangisa
Marks: 65
Special Instructions:
Part 1: Long Questions
Complete the answers on the question paper in the space provided.
45 Marks
You may use the back of the pages for rough work.
Follow the instructions given on the multiple choice answer sheet
Part 2: Multiple Choice
provided.
20 Marks
The use of pencil is preferable.
All multiple choice answers are to be completed on the multiple choice
answer sheet provided.
1. Answer ALL questions.
2. Round off your final answers to 3 decimal places.
3. Only financial/scientific calculators are allowed (no other electronic devices).
4. You may write in pencil (no remarks will be considered in this case).
5. Hand back ALL question papers and answer sheets when finished.
Surname and Initials
Student Number
Question
1
2
3
4
5
6
7
8
Total
Max
8
8
6
9
6
4
4
20
65
Mark
1
Part 1: Long Questions
[45]
Question 1
[8]
When playing songs on the radio, it is important that the songs are neither too long nor too short. A sample
of 30 songs, recorded by a certain artist is collected and the length of each song (in seconds) is recorded.
The data are given in the table below:
181
208
201
199
243
192
152
185
162
180
198
179
195
231
186
249
139
207
185
172
(a) Complete the following frequency distribution table:
Length of
song (sec)
[130, 150)
[150, 170)
[170, 190)
[190, 210)
[210, 230)
[230, 250)
Tally
Frequency
(f )
Relative
frequency
[5]
Size of pie
chart angle
Cumulative
Frequency (F )
(b) Construct a Ogive using the table in (a) and indicate the approximate value of the mode on the graph.
Label all axes clearly.
[3]
s
s
s
s
s
s
s
s
s
s
s
2
Question 2
[8]
An agronomist wants to determine the distribution of the sizes of potatoes in a crop at random locations. A
random sample of 15 potatoes was collected and weighed (grams). The weights of the potatoes were recorded
and are shown below:
230
215
224
223
245
237
237
199
215
207
228
213
222
228
237
(a) Calculate the arithmetic mean weight of the potatoes for the sample collected.
[2]
(b) Calculate the median weight of the potatoes for the sample collected.
[3]
(c) Calculate the mode weight of the potatoes for the sample collected.
[3]
(d) Comment on the skewness of the distributed weights of the potatoes (motivate your answer).
[2]
3
Question 3
[6]
A random sample of 50 first year students were asked to complete a test consisting of 20 basic mathematics
questions. The frequency distribution for the number of questions the students answered incorrectly is given
in the table below.
# Incorrect Answers
Frequency (f )
[0 - 4)
10
e
[4 - 8)
22
e
[8 - 12)
8
e
[12 - 16)
6
e
[16 - 20)
4
e
(Use the blank cells in this table to aid in your calculations)
(a) Calculate and interpret the first quartile of the number of questions that the students answered
incorrectly.
[3]
(b) Determine the 85th percentile of the number of questions that the students answered incorrectly. [3]
4
Question 4
[9]
Service calls received by a medical technologist constitute a Poisson process with a mean rate of 2.5 calls per
hour. Calculate the probability that there will be;
(a) no calls in a specific hour.
[2]
(b) at least one call in a specific hour.
[2]
(c) more than one call in 2 hours.
[4]
(d) How many calls would you expect in half hour period?
[1]
5
Question 5
[6]
A toy manufacturing company supplies batteries that last on average 18 hours with a variance of 9 (hours).
If a battery life is normally distributed, what are the following probabilities?
(a) that the battery life will be more than 12 hours.
[3]
(b) that the battery life will be between 13 and 19 hours
[3]
6
Question 6
[4]
The monthly profit generated by a medium-sized second-hand bookshop is thought to follow a normal
distribution. A random sample of 9 such medium-sized second-hand bookshops reveals a sample mean of
R13 000 with a sample standard deviation of R1 000. Construct a 99% confidence interval for the true
population mean monthly profit of medium-size second-hand bookshops.
Question 7
[4]
A wood processing company wants to determine a 99% confidence interval for the standard deviation of the
wood that is cut by their processing machine. A sample 30 logs was observed and it was found that the
average lengths were 10.2 m with a standard deviation of 3.7 m.
7
Part 2: Multiple Choice Questions
[20]
1. The relation between a parameter and a population is the same as the relation between
a) Descriptive statistics and inferential statistics
b) A dependent variable and an independent variable
c) A statistic and a sample
d) Quantitative and qualitative data
e) A statistic and a variable
[1]
2. The temperature (in ◦ C) in an air conditioned room would involve measurement on a(n) _____ scale.
a) nominal
b) ordinal
c) interval
d) ratio
e) none of the above
[1]
3. A scientist took daily measurements of the type of wildlife observed, the number of animals observed,
amount of rain and the maximum temperature. Which of the following is a qualitative variable?
a) Type of wildlife
b) Number of animals observed
c) Amount of rain
d) Maximum temperature
e) None of the above
[1]
4. Statistical techniques that summarise, organise and simplify data are classified as _____ statistics.
a) Population
b) Sample
c) Descriptive
d) Inferential
e) Classical
[1]
5. A sample of 30 individuals who smoke cigarettes was collected. Each individual was classified according
to how many cigarettes they smoked per day as either a “heavy smoker”, a “average smoker”, a “light
smoker”, or a “social smoker”. 12 of the sampled individuals were classified as “heavy smokers”, 7 as
“light smokers”, 3 as “average smokers” and the rest were classified as “social smokers”. If a pie chart
were to be made for this data, what would be the angle size for the “social smokers” category in the
pie chart?
a) 84◦
b) 36◦
c) 96◦
d) 144◦
e) none of the above
[1]
6. Which of the following graphical representations of data is used to graphically represent qualitative
data?
a) histograms
8
b) frequency polygons
c) ogives
d) pie charts
e) none of the above
[1]
For questions (7) to (9) consider the following scenario.
A random sample of 8 fraudulent transactions identified by a bank were investigated and the values (in R) of
the fraudulent transactions are given below
350
690
1000
540
125
600
220
1500
7. Calculate the mean value of the data above.
a) 456.38
b) 717.86
c) 628.13
d) 570.00
e) None of the above / cannot be calculated.
[1]
8. Calculate the median value of the data above.
a) 570.00
b) 600.00
c) 540.00
d) 575.00
e) None of the above / cannot be calculated
[1]
9. Calculate the first quartile of the data above.
a) 220.00
b) 350.00
c) 285.00
d) 252.50
e) None of the above / cannot be calculated
[1]
10. Consider the histogram below and select the correct order for the mean, median and mode.
9
a) I = Mode; II = Mean; III = Median
b) I = Median; II = Mean; III = Mode
c) I = Mean; II = Median; III = Mode
d) I = Mean; II = Mode; III = Median
e) I = Mode; II = Median; III = Mean
[1]
11. The following table provides a complete point probability distribution for the random variable X.
Calculate the missing value indicated by ???.
x
P (X = x)
0
0.25
1
???
2
0.05
3
0.06
4
0.53
a) 0.75
b) 0.56
c) 0.14
d) 0.11
e) None of the above / cannot be calculated.
For questions (12) and (13) consider the following scenario.
The following table provides a complete point probability distribution for the random variable X.
x
P (X = x)
0
0.10
2
0.23
4
0.42
6
0.20
8
0.05
12. What is E [X]?
a) 3.75
b) 3.84
c) 4.00
d) 0.23
e) none of the above
[1]
13. What is P (X > 8)?
a) 0.05
b) 0.95
c) 0.00
d) 0.10
e) none of the above
[1]
14. Suppose that X has a binomial distribution with n = 3 and p = 0.62. Calculate P (X ≤ 0).
a) 0.055
b) 0.945
c) 0.620
d) 0.830
e) None of the above / cannot be calculated.
[1]
15. Suppose it is known that the height of first year students in cm (X) has a normal distribution with
µ = 100 and σ = 15. A sample of 9 students is collected and their heights measured. Which of the
following statements is correct?
10
a) X̄ ∼ N (100; 15)
b) X̄ ∼ N (100; 1.67)
c) X̄ ∼ N (100; 25)
d) X̄ ∼ (100; 5)
e) none of the above
[1]
16. Which of the following properties of the standard normal distribution (Z) is correct? Note: z is any
real number, a and b are positive real numbers.
a) P (−a < Z < b) = P (Z < b) + P (Z < a) − 1
b) P (Z = z) > 0
c) P (a < Z < b) = P (Z < a) − P (Z < b)
d) P (Z > z) = 1 − P (Z < −z)
e) none of the above
[1]
17. The sampling error of the mean is defined as
a) 1 − p
b) x − xi
c) x̄ − p̂
d) x̄ − µ
e) none of the above
[1]
18. Suppose that a random variable Y has a normal distribution with a mean of 2 and a standard deviation
of 0.95. Calculate P (Y > 3.1).
a) 0.8599
b) 0.0485
c) 0.1292
d) 0.1401
e) none of the above
[1]
For questions (19) and (20) consider the following scenario.
A financial analyst is interested in the average return on a portfolio. In order to report this average return, a
confidence interval must be calculated.
19. In which of the following scenarios would the analyst use the standard normal distribution / table to
calculate the confidence interval for the mean return?
a) When n < 30, σ is known and the data are normally distributed.
b) When n < 30, σ is unknown and the data are not normally distributed.
c) When n < 30, σ is unknown and the data are normally distributed.
d) When n < 30, σ is known and the data are not normally distributed.
e) none of the above
11
[1]
20. Suppose now that the analyst uses the standard normal distribution to calculate the confidence interval
for the mean return. Which of the following intervals will be the narrowest?
a) A 99% confidence interval
b) A 97.5% confidence interval
c) A 95% confidence interval
d) A 90% confidence interval
e) All the confidence intervals are equal in length
12
[1]
STAV102 Formula Sheet
(
k = 1 + 3.3log (n) = 1 + 3.3
ln (n)
ln (10)
)
xmax − xmin
∑ k
n =
fi
c =
Rel. freq =
x̄ =
x̄ =
fi
n
n
1∑
xi
n i=1
∑
f i xi
∑
∑
s
2
=
s2 =
fi
√
∑
s =
√∑
s =
√∑
s =
CV
Me
Mo
Q1
∑
∑
x2i − n1 ( xi )2
(xi − x̄)2
=
n−1
n−1
∑
2
1 ∑
2
fi xi − n ( fi xi )
n−1
(xi − x̄)2
n−1
∑
x2i − n1 ( xi )2
n−1
∑
fi x2i − n1 ( fi xi )2
n−1
s
× 100
x̄
)
(
c n2 − Fi−1
= li +
fi
(
)
c (fi − fi−1 )
= li +
(fi − fi−1 ) + (fi − fi+1 )
(n
)
c 4 − Fi−1
= li +
fi
=
(
c
Q 3 = li +
3n
4 − Fi−1
)
fi
IQR = Q3 − Q1
LL = Q1 − 1.5 · IQR
U L = Q3 + 1.5 · IQR
( np
)
c 100
− Fi−1
Pp = l i +
fi
f
P (A) =
n
P (A ∪ B) = P (A) + P (B) − P (A ∩ B)
P (A ∩ B)
P (A|B) =
P (B)
P (A) = P (B1 ) P (A|B1 ) + · · · + P (Bn ) P (A|Bn )
P (Bk ) P (A|Bk )
P (Bk |A) =
P (B1 ) P (A|B1 ) + · · · + P (Bn ) P (A|Bn )
P (A ∩ B) = P (A) P (B|A)
P (A ∩ B) = P (A) P (B)
n!
n Cr =
r! (n − r)!
13
E [X] = µ =
V [X] = σ 2 =
P (X = x) =
∑
∑
xp (x)
x2 p (x) −
n Cr p
x
(∑
xp (x)
)2
(1 − p)n−x
E [X] = np
V [X] = np (1 − p)
µx e−µ
P (X = x) =
x!
E [X] = V [X] = µ
P (Z < −z) = P (Z > z)
P (Z > z) = 1 − P (Z ≤ z)
X −µ
Z =
σ
σ
σX̄ = √
n
X −µ
Z =
σX̄
X −µ
Z =
σ/√n
X
p̂ =
n
√
σp =
Z =
Z =
p (1 − p)
n
p̂ − p
σp
p̂ − p
√
[
p(1−p)
n
]
σ
x̄ ± z1−α/2 √
n
[
]
s
= x̄ ± z1−α/2 √
n
CI (µ)1−α =
CI (µ)1−α
[
CI (µ)1−α =
s
x̄ ± tn−1;1−α/2 √
n

√
CI (p)1−α = p̂ ± z1−α/2
(
CI σ
2
[
)
1−α
=
]

p̂(1 − p̂) 
n
(n − 1) s2 (n − 1) s2
;
χ2n−1;1−α/2 χ2n−1;α/2
(
)
z1−α/2 σ 2
n =
e
(
)
z1−α/2 2
n =
p(1 − p)
e
14
]
z
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
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
0.00
0.5000
0.5398
0.5793
0.6179
0.6554
0.6915
0.7257
0.7580
0.7881
0.8159
0.8413
0.8643
0.8849
0.9032
0.9192
0.9332
0.9452
0.9554
0.9641
0.9713
0.9772
0.9821
0.9861
0.9893
0.9918
0.9938
0.9953
0.9965
0.9974
0.9981
0.9987
0.9990
0.9993
0.9995
0.9997
0.01
0.5040
0.5438
0.5832
0.6217
0.6591
0.6950
0.7291
0.7611
0.7910
0.8186
0.8438
0.8665
0.8869
0.9049
0.9207
0.9345
0.9463
0.9564
0.9649
0.9719
0.9778
0.9826
0.9864
0.9896
0.9920
0.9940
0.9955
0.9966
0.9975
0.9982
0.9987
0.9991
0.9993
0.9995
0.9997
Standard Normal Probabilities P (Z ≤ z)
0.02
0.03
0.04
0.05
0.06
0.07
0.5080 0.5120 0.5160 0.5199 0.5239 0.5279
0.5478 0.5517 0.5557 0.5596 0.5636 0.5675
0.5871 0.5910 0.5948 0.5987 0.6026 0.6064
0.6255 0.6293 0.6331 0.6368 0.6406 0.6443
0.6628 0.6664 0.6700 0.6736 0.6772 0.6808
0.6985 0.7019 0.7054 0.7088 0.7123 0.7157
0.7324 0.7357 0.7389 0.7422 0.7454 0.7486
0.7642 0.7673 0.7704 0.7734 0.7764 0.7794
0.7939 0.7967 0.7995 0.8023 0.8051 0.8078
0.8212 0.8238 0.8264 0.8289 0.8315 0.8340
0.8461 0.8485 0.8508 0.8531 0.8554 0.8577
0.8686 0.8708 0.8729 0.8749 0.8770 0.8790
0.8888 0.8907 0.8925 0.8944 0.8962 0.8980
0.9066 0.9082 0.9099 0.9115 0.9131 0.9147
0.9222 0.9236 0.9251 0.9265 0.9279 0.9292
0.9357 0.9370 0.9382 0.9394 0.9406 0.9418
0.9474 0.9484 0.9495 0.9505 0.9515 0.9525
0.9573 0.9582 0.9591 0.9599 0.9608 0.9616
0.9656 0.9664 0.9671 0.9678 0.9686 0.9693
0.9726 0.9732 0.9738 0.9744 0.9750 0.9756
0.9783 0.9788 0.9793 0.9798 0.9803 0.9808
0.9830 0.9834 0.9838 0.9842 0.9846 0.9850
0.9868 0.9871 0.9875 0.9878 0.9881 0.9884
0.9898 0.9901 0.9904 0.9906 0.9909 0.9911
0.9922 0.9925 0.9927 0.9929 0.9931 0.9932
0.9941 0.9943 0.9945 0.9946 0.9948 0.9949
0.9956 0.9957 0.9959 0.9960 0.9961 0.9962
0.9967 0.9968 0.9969 0.9970 0.9971 0.9972
0.9976 0.9977 0.9977 0.9978 0.9979 0.9979
0.9982 0.9983 0.9984 0.9984 0.9985 0.9985
0.9987 0.9988 0.9988 0.9989 0.9989 0.9989
0.9991 0.9991 0.9992 0.9992 0.9992 0.9992
0.9994 0.9994 0.9994 0.9994 0.9994 0.9995
0.9995 0.9996 0.9996 0.9996 0.9996 0.9996
0.9997 0.9997 0.9997 0.9997 0.9997 0.9997
Standard Normal Critical Values
α
(1 − α)
α
z1−α z1−α/2
2
0.9
0.1
0.05 1.282 1.645
0.95
0.05 0.025 1.645 1.960
0.98
0.02 0.01 2.054 2.326
0.99
0.01 0.005 2.326 2.576
15
0.08
0.5319
0.5714
0.6103
0.6480
0.6844
0.7190
0.7517
0.7823
0.8106
0.8365
0.8599
0.8810
0.8997
0.9162
0.9306
0.9429
0.9535
0.9625
0.9699
0.9761
0.9812
0.9854
0.9887
0.9913
0.9934
0.9951
0.9963
0.9973
0.9980
0.9986
0.9990
0.9993
0.9995
0.9996
0.9997
0.09
0.5359
0.5753
0.6141
0.6517
0.6879
0.7224
0.7549
0.7852
0.8133
0.8389
0.8621
0.8830
0.9015
0.9177
0.9319
0.9441
0.9545
0.9633
0.9706
0.9767
0.9817
0.9857
0.9890
0.9916
0.9936
0.9952
0.9964
0.9974
0.9981
0.9986
0.9990
0.9993
0.9995
0.9997
0.9998
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
35
40
45
50
60
70
80
90
100
∞
0.75
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.682
0.681
0.680
0.679
0.679
0.678
0.678
0.677
0.677
0.674
Students t-Distribution Critical Values
Lower tail probability (1 − α)
0.9
0.95 0.975
0.99
0.995 0.9975
3.078 6.314 12.706 31.821 63.657 127.321
1.886 2.920 4.303
6.965
9.925
14.089
1.638 2.353 3.182
4.541
5.841
7.453
1.533 2.132 2.776
3.747
4.604
5.598
1.476 2.015 2.571
3.365
4.032
4.773
1.440 1.943 2.447
3.143
3.707
4.317
1.415 1.895 2.365
2.998
3.499
4.029
1.397 1.860 2.306
2.896
3.355
3.833
1.383 1.833 2.262
2.821
3.250
3.690
1.372 1.812 2.228
2.764
3.169
3.581
1.363 1.796 2.201
2.718
3.106
3.497
1.356 1.782 2.179
2.681
3.055
3.428
1.350 1.771 2.160
2.650
3.012
3.372
1.345 1.761 2.145
2.624
2.977
3.326
1.341 1.753 2.131
2.602
2.947
3.286
1.337 1.746 2.120
2.583
2.921
3.252
1.333 1.740 2.110
2.567
2.898
3.222
1.330 1.734 2.101
2.552
2.878
3.197
1.328 1.729 2.093
2.539
2.861
3.174
1.325 1.725 2.086
2.528
2.845
3.153
1.323 1.721 2.080
2.518
2.831
3.135
1.321 1.717 2.074
2.508
2.819
3.119
1.319 1.714 2.069
2.500
2.807
3.104
1.318 1.711 2.064
2.492
2.797
3.091
1.316 1.708 2.060
2.485
2.787
3.078
1.315 1.706 2.056
2.479
2.779
3.067
1.314 1.703 2.052
2.473
2.771
3.057
1.313 1.701 2.048
2.467
2.763
3.047
1.311 1.699 2.045
2.462
2.756
3.038
1.310 1.697 2.042
2.457
2.750
3.030
1.306 1.690 2.030
2.438
2.724
2.996
1.303 1.684 2.021
2.423
2.704
2.971
1.301 1.679 2.014
2.412
2.690
2.952
1.299 1.676 2.009
2.403
2.678
2.937
1.296 1.671 2.000
2.390
2.660
2.915
1.294 1.667 1.994
2.381
2.648
2.899
1.292 1.664 1.990
2.374
2.639
2.887
1.291 1.662 1.987
2.368
2.632
2.878
1.290 1.660 1.984
2.364
2.626
2.871
1.282 1.645 1.960
2.326
2.576
2.807
16
0.999
318.309
22.327
10.215
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
3.610
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.340
3.307
3.281
3.261
3.232
3.211
3.195
3.183
3.174
3.090
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
70
80
0.005
0
0.01
0.072
0.21
0.41
0.68
0.99
1.34
1.73
2.16
2.6
3.07
3.57
4.07
4.6
5.14
5.7
6.26
6.84
7.43
8.03
8.64
9.26
9.89
10.52
11.16
11.81
12.46
13.12
13.79
20.71
27.99
35.53
43.28
51.17
0.01
0
0.02
0.115
0.3
0.55
0.87
1.24
1.65
2.09
2.56
3.05
3.57
4.11
4.66
5.23
5.81
6.41
7.01
7.63
8.26
8.9
9.54
10.2
10.86
11.52
12.2
12.88
13.56
14.26
14.95
22.16
29.71
37.48
45.44
53.54
χ2 distribution critical values
(1 − α)
0.025 0.05
0.1
0.9
0.95
0.001 0.004 0.016 2.71
3.84
0.051 0.103 0.211 4.61
5.99
0.216
0.35
0.58
6.25
7.81
0.48
0.71
1.06
7.78
9.49
0.83
1.15
1.61
9.24
11.07
1.24
1.64
2.2
10.64 12.59
1.69
2.17
2.83 12.02 14.07
2.18
2.73
3.49 13.36 15.51
2.7
3.33
4.17 14.68 16.92
3.25
3.94
4.87 15.99 18.31
3.82
4.57
5.58 17.28 19.68
4.4
5.23
6.3
18.55 21.03
5.01
5.89
7.04 19.81 22.36
5.63
6.57
7.79 21.06 23.68
6.26
7.26
8.55 22.31
25
6.91
7.96
9.31 23.54
26.3
7.56
8.67 10.09 24.77 27.59
8.23
9.39 10.86 25.99 28.87
8.91
10.12 11.65 27.2
30.14
9.59
10.85 12.44 28.41 31.41
10.28 11.59 13.24 29.62 32.67
10.98 12.34 14.04 30.81 33.92
11.69 13.09 14.85 32.01 35.17
12.4
13.85 15.66 33.2
36.42
13.12 14.61 16.47 34.38 37.65
13.84 15.38 17.29 35.56 38.89
14.57 16.15 18.11 36.74 40.11
15.31 16.93 18.94 37.92 41.34
16.05 17.71 19.77 39.09 42.56
16.79 18.49 20.6 40.26 43.77
24.43 26.51 29.05 51.81 55.76
32.36 34.76 37.69 63.17
67.5
40.48 43.19 46.46 74.4
79.08
48.76 51.74 55.33 85.53 90.53
57.15 60.39 64.28 96.58 101.88
17
0.975
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
83.3
95.02
106.63
0.99
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
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
100.43
112.33
0.995
7.88
10.6
12.84
14.86
16.75
18.55
20.28
21.95
23.59
25.19
26.76
28.3
29.82
31.32
32.8
34.27
35.72
37.16
38.58
40
41.4
42.8
44.18
45.56
46.93
48.29
49.64
50.99
52.34
53.67
66.77
79.49
91.95
104.21
116.32