STAT 211 Business Statistics I – Term 122
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICS & STATISTICS
DHAHRAN, SAUDI ARABIA
STAT 211: BUSINESS STATISTICS I
Semester 122
Final Exam
Thursday May 16, 2013
Allowed time 7:00 pm – 9:30 pm
Please circle your instructor’s name:
section number
Adnan Jabbar
Sec 1: (9:00 – 9:50)
Musawar A. Malik
Sec 3: (07:00 –07:50)
Sec 2 : (10:00 – 10:50)
[
Name:
Student ID#:
Serial #:
Directions:
1) You must show all work to obtain full credit for questions on this exam.
2) DO NOT round your answers at each step. Round answers only if necessary at your final
step to 4 decimal places.
3) You are allowed to use electronic calculators and other reasonable writing accessories that
help write the exam. Try to define events, formulate problem and solve.
4) Do not keep your mobile with you during the exam, turn off your mobile and leave it aside.
Q. No Marks
Marks
Obtained
Q. No
Marks
Q1
10
Q11
5
Q2
12
Q12
4
Q3
7
Q13
3
Q4
3
Q14
8
Q5
4
Q15
10
Q6
3
Q16
5
Q7
3
Q17
3
Q8
3
Q18
7
Q9
5
Q10
5
Total
100
Marks
Obtained
1
STAT 211 Business Statistics I – Term 122
2
1. (10 points).
(i)The estimation of the population average family expenditure on food based on the sample average
expenditure of 1,000 families is an example of
(a)
(b)
(c)
(d)
Inferential statistics.
Descriptive statistics.
A parameter.
A statistic.
(ii) Which of the following is most likely a population as opposed to a sample?
(a) Respondents to a newspaper survey.
(b) The first 5 students completing an assignment.
(c) Every third person to arrive at the bank.
(d) Registered voters in a county.
(iii) Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But
incidentals, such as textbook costs, are rarely considered. A researcher at Drummond University wishes to
estimate the textbook costs of first-year students at Drummond. To do so, she monitored the textbook cost
of 250 first-year students and found that their average textbook cost was $300 per semester. Identify the
sample in the study.
(a)
(b)
(c)
(d)
All Drummond University students.
All college students.
All first-year Drummond University students.
The 250 students that were monitored.
(iv) John was working on a project to look at global warming and accessed an Internet site where he
captured average global surface temperatures from 1866. Which of the four methods of data collection was
he using?
(a)
(b)
(c)
(d)
Published sources.
Experimentation.
Surveying.
Observation
STAT 211 Business Statistics I – Term 122
3
(v) The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to
find out the proportion of students at her university who visited campus bars on the weekend before the final
exam week. Her assistant took a random sample of 250 students and computed the portion of students in the
sample who visited campus bars on the weekend before the final exam. The portion of all students at her
university who visited campus bars on the weekend before the final exam week is an example of
(a)
(b)
(c)
(d)
A categorical random variable.
A discrete random variable.
A continuous random variable.
A parameter.
(vi) True or False: The amount of coffee consumed by an individual in a day is an example of a discrete
numerical variable.
(vii) True or False: The answer to the question “How many hours on average do you spend watching TV
every week?” is an example of a ratio scaled variable.
(viii) True or False: Compiling the number of registered voters who turned out to vote for the primary in
Iowa is an example of descriptive statistics.
(ix) The Dean of Students conducted a survey on campus. Grade point average (GPA) is an
example of a _____________________ numerical variable.
(x) The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A
sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were
discharged during the year 1997. Using the information obtained from the sample to predict population
characteristics with respect to malpractice litigation is an example
of _____________________.
STAT 211 Business Statistics I – Term 122
4
2. An European distribution company surveyed 53 of its mid-level managers. The survey obtained the
ages of these managers, which later were organized into the frequency distribution shown.
a. Determine the class midpoint, relative frequency, and cumulative frequency for these data. (6
points).
b. Construct a frequency histogram and comment on the shape. (3 points).
c. Calculate the approximate mean for this data. (3 points).
Class Interval
Frequency
20-under 25
8
25-under 30
6
30-under 35
5
35-under 40
12
40-under 45
15
45-under 50
7
Midpoint
Relative
frequency
Cumulative
frequency
STAT 211 Business Statistics I – Term 122
5
3. The following data represent complaints about hotel rooms:
Reason
Number
Room Dirty
32
Room not stocked
17
Room not ready
12
Room too noisy
10
Room needs maintenance
17
Room has too few beds
9
Room doesn’t have promised 7
features
No special accommodations
2
(a) Construct a Pareto chart. (5 points).
(b) What reasons for complaints do you think the hotel should focus on if it wants to reduce the number of
complaints? Explain. (2 points).
STAT 211 Business Statistics I – Term 122
6
4. A company has 140 employees, of which 30 are supervisors. Eighty of the employees are married,
and 20% of the married employees are supervisors. If a company employee is randomly selected,
what is the probability that the employee is married and is a supervisor? (3 points).
5. Suppose that of all individuals buying a certain personal computer, 60% include a word processing
program in their purchase, 40% include a spreadsheet program, and 30% include both types of
programs. Consider randomly selecting a purchaser and let A = (word processing program included)
and B = (spreadsheet program included).
a. Find the probability that a word processing program was included given that the selected individual
included a spreadsheet program. (2 points).
b. Find the probability that a spreadsheet program was included given that the selected individual
included a word processing program. (2 points).
6. Five percent of all DVD players manufactured by a large electronics company are defective. A
quality control inspector randomly selects three DVD players from the production line. What is the
probability that exactly one of these three DVD players is defective? (3 points).
STAT 211 Business Statistics I – Term 122
7
7. Brown Manufacturing makes auto parts that are sold to auto dealers. Last week the company
shipped 25 auto parts to a dealer. Later, it found out that 5 of those parts were defective. By the time
the company manager contacted the dealer, 4 auto parts from that shipment had already been sold.
What is the probability that 3 of those 4 parts were good parts and 1 was defective? (3 points).
8. A washing machine in a Laundromat breaks down an average of three times per month, find the
probability that during the next month this machine will have at most one breakdown. (3 points).
9. According to Sallie Mae surveys and Credit Bureau data, college students carried an average of
$3173 credit card debt in 2008. Suppose the probability distribution of the current credit card debts
for all college students has normal distribution with a mean of $3173 and the standard deviation of
$800. What is the probability that a credit card debt for a randomly selected college student is
between $2109 and $3605? (5 points).
STAT 211 Business Statistics I – Term 122
8
10. According to an estimate, 45% of the people in the United States have at least one credit card. If a
random sample of 30 persons is selected, what is the probability that at least 19 of them will have at
least one credit card? (5 points).
11. According to Sallie Mae surveys and Credit Bureau data, college students carried an average of
$3173 credit card debt in 2008. Suppose the probability distribution of the current credit card debts
of college students in the United States is unknown but its mean is $3173 and the standard deviation
is $750. What is the probability that the mean of the current credit card debts for a random sample of
400 U.S. college students is within $70 of the population mean? (5 points).
12. A major department store chain is interested in estimating the average amount its credit card
customers spent on their first visit to the chain’s new store in the mall. Fifty credit card accounts
were randomly sampled and analyzed with the following results: X  $50.50 & s 2  400 . Construct
a 95% confidence interval for the average amount its credit card customers spent on their first visit
to the chain’s new store in the mall. (4 points).
STAT 211 Business Statistics I – Term 122
9
13. A manager wishes to estimate a population mean using a 99% confidence interval estimate that has
a margin of error of ±45.0. If the population standard deviation is thought to be 680, what is the
required sample size? (3 points).
14. To become an actuary, it is necessary to pass a series of 10 exams, including the most important one,
an exam in probability and statistics. An insurance company wants to estimate the mean score on
this exam for actuarial students who have enrolled in a special study program. They take a sample of
8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This
sample will be used to calculate a 90% confidence interval for the mean score for actuarial students
in the special study program.
a. What is the critical value used in constructing a 90% confidence interval. (1 point).
b. What is the standard deviation of the data? (2 points).
c. What is the standard error of the estimate? (1 point).
d. What is the margin of error? (1 point).
e. What is lower limit of the interval? (1 point).
f. What is the range of the interval? (1 points).
g. What assumption do you need to make about the population of interest to construct the interval. (1
points).
STAT 211 Business Statistics I – Term 122
10
15. Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these
gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from
supplier 1 results in mean = 290 and S.D = 12, while another random sample of 16 gears from the
second supplier results in mean = 321 and S.D = 22. A.
a. Calculate a 99% confidence interval for the difference in mean impact strength of gears from these
two suppliers. Also interpret your result. (7 points).
b. What assumptions are required to do part a. (3 points).
16. An economist is interested in studying the incomes of consumers in a particular region. The
population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in
an average income of $15,000. What is the width of the 90% confidence interval? (5 points).
STAT 211 Business Statistics I – Term 122
11
17. The head of a business department is interested in estimating the proportion of students entering
the department who will choose the new marketing strategy option. A preliminary sample indicates
that the proportion will be around 0.25. Therefore, what size sample should the department head take
if she wants to be 95% confident that the estimate is within 0.10 of the true proportion? (3 points).
18. A corporation randomly selects 150 salespeople and finds that 66% who have never taken a selfimprovement course would like such a course. The firm did a similar study 10 years ago in which
60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are
assumed to be independent random samples. Let 1 and  2 represent the true proportion of workers
who would like to attend a self-improvement course in the recent study and the past study,
respectively.
a. Construct a 95% confidence interval estimate of the difference in proportion of workers who would
like to attend a self-improvement course in the recent study and the past study. (5 points).
b. Write the assumptions needed to do part (a). (2 points).
STAT 211 Business Statistics I – Term 122
12
The cumulative Standard Normal distribution
Entry represented area under the cumulative standardized normal
distribution from - ∞ to Z
Cumulative Probabilities
Z
 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
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0013
0.0013
0.0013
0.0012
0.0012
0.0011
0.0011
0.0011
0.0010
0.0010
0.0019
0.0018
0.0018
0.0017
0.0016
0.0016
0.0015
0.0015
0.0014
0.0014
0.0026
0.0025
0.0024
0.0023
0.0023
0.0022
0.0021
0.0021
0.0020
0.0019
0.0035
0.0034
0.0033
0.0032
0.0031
0.0030
0.0029
0.0028
0.0027
0.0026
0.0047
0.0045
0.0044
0.0043
0.0041
0.0040
0.0039
0.0038
0.0037
0.0036
0.0062
0.0060
0.0059
0.0057
0.0055
0.0054
0.0052
0.0051
0.0049
0.0048
0.0082
0.0080
0.0078
0.0075
0.0073
0.0071
0.0069
0.0068
0.0066
0.0064
0.0107
0.0104
0.0102
0.0099
0.0096
0.0094
0.0091
0.0089
0.0087
0.0084
0.0139
0.0136
0.0132
0.0129
0.0125
0.0122
0.0119
0.0116
0.0113
0.0110
0.0179
0.0174
0.0170
0.0166
0.0162
0.0158
0.0154
0.0150
0.0146
0.0143
0.0228
0.0222
0.0217
0.0212
0.0207
0.0202
0.0197
0.0192
0.0188
0.0183
0.0287
0.0281
0.0274
0.0268
0.0262
0.0256
0.0250
0.0244
0.0239
0.0233
0.0359
0.0351
0.0344
0.0336
0.0329
0.0322
0.0314
0.0307
0.0301
0.0294
0.0446
0.0436
0.0427
0.0418
0.0409
0.0401
0.0392
0.0384
0.0375
0.0367
0.0548
0.0537
0.0526
0.0516
0.0505
0.0495
0.0485
0.0475
0.0465
0.0455
0.0668
0.0655
0.0643
0.0630
0.0618
0.0606
0.0594
0.0582
0.0571
0.0559
0.0808
0.0793
0.0778
0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
0.0968
0.0951
0.0934
0.0918
0.0901
0.0885
0.0869
0.0853
0.0838
0.0823
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.1020
0.1003
0.0985
0.1357
0.1335
0.1314
0.1292
0.1271
0.1251
0.1230
0.1210
0.1190
0.1170
0.1587
0.1562
0.1539
0.1515
0.1492
0.1469
0.1446
0.1423
0.1401
0.1379
0.1841
0.1814
0.1788
0.1762
0.1736
0.1711
0.1685
0.1660
0.1635
0.1611
0.2119
0.2090
0.2061
0.2033
0.2005
0.1977
0.1949
0.1922
0.1894
0.1867
0.2420
0.2389
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.2514
0.2483
0.2451
0.3085
0.3050
0.3015
0.2981
0.2946
0.2912
0.2877
0.2843
0.2810
0.2776
0.3446
0.3409
0.3372
0.3336
0.3300
0.3264
0.3228
0.3192
0.3156
0.3121
0.3821
0.3783
0.3745
0.3707
0.3669
0.3632
0.3594
0.3557
0.3520
0.3483
0.4207
0.4168
0.4129
0.4090
0.4052
0.4013
0.3974
0.3936
0.3897
0.3859
0.4602
0.4562
0.4522
0.4483
0.4443
0.4404
0.4364
0.4325
0.4286
0.4247
0.5000
0.4960
0.4920
0.4880
0.4840
0.4801
0.4761
0.4721
0.4681
0.4641
STAT 211 Business Statistics I – Term 122
13
The cumulative Standard Normal distribution
Entry represented area under the cumulative standardized normal
distribution from - ∞ to Z
Cumulative Probabilities
Z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
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
STAT 211 Business Statistics I – Term 122
14
For a particular number of degrees of freedom, entry represents the
critical value of corresponding to a specified upper – tail area (  )
Cumulative Probabilities
0.55
0.65
0.75
0.85
0.9
0.95
0.965
0.975
0.99
0.995
Upper Tail Areas
d.f.
0.45
0.35
0.25
0.15
0.1
0.05
0.035
0.025
0.01
0.005
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.1584
0.1421
0.1366
0.1338
0.1322
0.1311
0.1303
0.1297
0.1293
0.1289
0.1286
0.1283
0.1281
0.1280
0.1278
0.1277
0.1276
0.1274
0.1274
0.1273
0.1272
0.1271
0.1271
0.1270
0.1269
0.1269
0.1268
0.1268
0.1268
0.1267
0.1267
0.1266
0.1266
0.1265
0.1265
0.1264
0.1264
0.1264
0.1263
0.1263
0.1262
0.1261
0.1261
0.1260
0.5095
0.4447
0.4242
0.4142
0.4082
0.4043
0.4015
0.3995
0.3979
0.3966
0.3956
0.3947
0.3940
0.3933
0.3928
0.3923
0.3919
0.3915
0.3912
0.3909
0.3906
0.3904
0.3902
0.3900
0.3898
0.3896
0.3894
0.3893
0.3892
0.3890
0.3888
0.3886
0.3884
0.3882
0.3881
0.3880
0.3878
0.3877
0.3876
0.3875
0.3872
0.3869
0.3867
0.3866
1.0000
0.8165
0.7649
0.7407
0.7267
0.7176
0.7111
0.7064
0.7027
0.6998
0.6974
0.6955
0.6938
0.6924
0.6912
0.6901
0.6892
0.6884
0.6876
0.6870
0.6864
0.6858
0.6853
0.6848
0.6844
0.6840
0.6837
0.6834
0.6830
0.6828
0.6822
0.6818
0.6814
0.6810
0.6807
0.6804
0.6801
0.6799
0.6796
0.6794
0.6786
0.6780
0.6776
0.6772
1.9626
1.3862
1.2498
1.1896
1.1558
1.1342
1.1192
1.1081
1.0997
1.0931
1.0877
1.0832
1.0795
1.0763
1.0735
1.0711
1.0690
1.0672
1.0655
1.0640
1.0627
1.0614
1.0603
1.0593
1.0584
1.0575
1.0567
1.0560
1.0553
1.0547
1.0535
1.0525
1.0516
1.0508
1.0500
1.0494
1.0488
1.0483
1.0478
1.0473
1.0455
1.0442
1.0432
1.0424
3.0777
1.8856
1.6377
1.5332
1.4759
1.4398
1.4149
1.3968
1.3830
1.3722
1.3634
1.3562
1.3502
1.3450
1.3406
1.3368
1.3334
1.3304
1.3277
1.3253
1.3232
1.3212
1.3195
1.3178
1.3163
1.3150
1.3137
1.3125
1.3114
1.3104
1.3086
1.3070
1.3055
1.3042
1.3031
1.3020
1.3011
1.3002
1.2994
1.2987
1.2958
1.2938
1.2922
1.2910
6.3138
2.9200
2.3534
2.1318
2.0150
1.9432
1.8946
1.8595
1.8331
1.8125
1.7959
1.7823
1.7709
1.7613
1.7531
1.7459
1.7396
1.7341
1.7291
1.7247
1.7207
1.7171
1.7139
1.7109
1.7081
1.7056
1.7033
1.7011
1.6991
1.6973
1.6939
1.6909
1.6883
1.6860
1.6839
1.6820
1.6802
1.6787
1.6772
1.6759
1.6706
1.6669
1.6641
1.6620
9.0579
3.5782
2.7626
2.4559
2.2974
2.2011
2.1365
2.0902
2.0554
2.0283
2.0067
1.9889
1.9742
1.9617
1.9509
1.9417
1.9335
1.9264
1.9200
1.9143
1.9092
1.9045
1.9003
1.8965
1.8929
1.8897
1.8867
1.8839
1.8813
1.8789
1.8746
1.8708
1.8674
1.8644
1.8617
1.8593
1.8571
1.8551
1.8532
1.8516
1.8448
1.8401
1.8365
1.8337
12.7062
4.3027
3.1824
2.7764
2.5706
2.4469
2.3646
2.3060
2.2622
2.2281
2.2010
2.1788
2.1604
2.1448
2.1314
2.1199
2.1098
2.1009
2.0930
2.0860
2.0796
2.0739
2.0687
2.0639
2.0595
2.0555
2.0518
2.0484
2.0452
2.0423
2.0369
2.0322
2.0281
2.0244
2.0211
2.0181
2.0154
2.0129
2.0106
2.0086
2.0003
1.9944
1.9901
1.9867
31.8205
6.9646
4.5407
3.7469
3.3649
3.1427
2.9980
2.8965
2.8214
2.7638
2.7181
2.6810
2.6503
2.6245
2.6025
2.5835
2.5669
2.5524
2.5395
2.5280
2.5176
2.5083
2.4999
2.4922
2.4851
2.4786
2.4727
2.4671
2.4620
2.4573
2.4487
2.4411
2.4345
2.4286
2.4233
2.4185
2.4141
2.4102
2.4066
2.4033
2.3901
2.3808
2.3739
2.3685
63.6567
9.9248
5.8409
4.6041
4.0321
3.7074
3.4995
3.3554
3.2498
3.1693
3.1058
3.0545
3.0123
2.9768
2.9467
2.9208
2.8982
2.8784
2.8609
2.8453
2.8314
2.8188
2.8073
2.7969
2.7874
2.7787
2.7707
2.7633
2.7564
2.7500
2.7385
2.7284
2.7195
2.7116
2.7045
2.6981
2.6923
2.6870
2.6822
2.6778
2.6603
2.6479
2.6387
2.6316
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STAT 211 Business Statistics I – Term 122
15
Some Useful Formulas
 S
x
x

2

n 1
x
2
 n (x ) 2
n 1

P(A or B) = P(A U B) = P(A) + P(B) – P(A∩B)

P(A ∩ B ' ) = P(A) – P(A ∩ B)



P  A | B 
P  A  B
P  B



PB j | A 
P  A

k
 P A | B PB 
i
P x  
n!
x

x ! n  x !
for j  1,2,..., k
P 0  x  a   1  e
a
σ
n
 (1   )
 μ p   , σp 
,
n
 x  zα/2 σ
n

μ x  μ , σx 
 x1  x 2   z  /2

 x1  x 2   t  ,n1  n2 2 sp
n x
  E  X   n  ,   n 1   
  t x e  t
P x  
,  t ,   t
x!
 N  A  A 
N X
X
 n  x  x 
C
nx C x
 
P x  

N
N 
Cn
n
 
 1
if a  x  b

f  x   b  a
,
0
otherwise

s12 s22

n1 n 2

i
1 
2
σ12 σ22

n1
n2
 x1  x 2   z  /2

PA | B j PB j 
e
σ
z
   /2 
 e 
p (1  p )
n
2
z  (1   )
n   /2 2
e
P(A ∩ B) = P(A) × P(B | A) = P(B) × P(A|B)
PB j  A
, n 1
2
z 2 /2 σ 2
2
s
n
p  z  /2

, P  B  0
a  c  d  b P c  X  d   (d c ) f (x )

n


i 1

x t 

2
1
1
,

n1 n 2
where
sp 

 n1  1 s12   n 2  1 s22
n1  n 2  2
 x1  x 2   t /2, v
s12 s 2 2

, where
n1 n 2
2
 s12 s 2 2 



n1 n 2 

v 
2
2
 s12   s 2 2 
  

 n1    n 2 
n1  1
n2 1

d  t
2
, n 1
sd
n

 p1  p2   z  /2
where
x
p1  1 ,
n1
p2 
x2
n2
p1 (1  p1 ) p 2 (1  p 2 )

n1
n2