Quantitative Methods for Business

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Prob 1

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
1. (4pts) The following table contains measurements of the inside diameters of machined parts (0.01 mm).
Observation
Sample 1 2 3 4
1 15 11 6 9 a. Calculate the sample means for each of the 10 samples.
2 14 4 10 6
3 7 10 9 11
4 8 6 9 13
5 14 8 9 12
6 9 10 7 13
7 15 10 12 12
8 14 16 11 10
9 11 7 16 10
10 11 14 11 12
b. Calculate the overall process mean, x-bar.

Prob 2

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
2. (5pts) Data-entry clerks at a large insurance company key in thousands of insurance records each day. Samples
of work of 20 experienced clerks is shown in the table below. 12 Records entered by each clerk were carefully
examined to determine if they contained errors.
Clerk Sample Size x-bar, Avg # errors per page
1 12 0.50 Process mean = 0.30 and process std deviation = 0.231. Calculate the
2 12 0.42 3-SEM upper and lower control limits for an x-bar control chart of data entry.
3 12 0.00 [You don't need to plot a chart.]
4 12 0.08
5 12 0.33
6 12 0.17
7 12 0.42
8 12 0.25
9 12 0.25
10 12 0.17
11 12 0.50
12 12 0.08
13 12 0.00
14 12 0.58
15 12 0.42
16 12 0.33
17 12 0.83
18 12 0.25
19 12 0.00
20 12 0.33
240 0.30

Prob 3

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
3. (6pts) A pharmaceutical manufacturer must control the concentration of active ingredient in a chemical process.
The optimum concentration is 10% and the following data is collected in 12 sample sets.
Observation
Sample 1 2 3
1 10.22 10.31 9.79 10.11 process mean = 10.16
2 10.25 10.33 10.12 10.23 process std deviation = 0.35
3 10.37 9.92 10.80 10.36 UCL = 10.67
4 10.46 9.94 10.26 10.22 LCL = 9.65
5 10.06 9.39 9.66 9.70
6 10.59 10.15 10.31 10.35
7 10.82 10.80 10.23 10.62 a. Construct/plot an x-bar control chart of the chemical process.
8 9.79 10.14 10.20 10.04
9 10.52 9.50 9.43 9.82
10 10.13 10.69 10.15 10.32
11 9.88 10.32 10.31 10.17 b. Is the process in control? Why or why not?
12 10.00 10.10 9.92 10.01

Prob 4

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
4. (4pts) A value, x = 18.8, is sampled from a normal distribution having mean = 32.7 and standard deviation = 6.4.
a. Calculate the Z-score for x = 18.8
b. Explain the meaning of the Z-score value you calculated.

Prob 5

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
5. (6pts) An online advertiser measures the "stickiness" of its ads by the browse duration of a webpage. Browsing data is sampled
throughout the advertisement's run as a check of the host's system reliability. The following data is a small subset of such
a sampling of ad duration (in seconds).
Obs Duration
1 0.539 a.  Calculate the sample mean and sample standard deviation of the 300 observations.
2 0.626
3 2.752
4 2.400
5 4.825
6 0.086
7 2.370 b. Assign a Z-score to each sample observation.
8 1.453
9 5.836
10 0.268
11 3.935 c. The advertiser classifies any duration greater than 3s distant as an outlier.
12 4.901 Identify all 3s outliers in the data.
13 1.900
14 0.428
15 1.968
16 9.174
17 0.154
18 0.829
19 10.026
20 0.554
21 0.663
22 0.152
23 1.270
24 0.061
25 0.722
26 5.246
27 2.665
28 1.208
29 0.658
30 2.374
31 3.184
32 1.504
33 0.051
34 0.618
35 1.406
36 0.910
37 3.866
38 1.462
39 3.056
40 3.554
41 0.426
42 1.586
43 1.367
44 0.344
45 1.649
46 0.234
47 1.434
48 1.725
49 10.241
50 2.539
51 1.019
52 0.281
53 11.229
54 8.038
55 2.410
56 8.192
57 3.608
58 3.619
59 1.290
60 1.145
61 1.228
62 6.668
63 1.559
64 4.799
65 0.391
66 13.961
67 4.260
68 2.087
69 0.052
70 1.767
71 10.316
72 4.562
73 4.803
74 5.993
75 0.600
76 0.891
77 5.798
78 1.318
79 0.169
80 1.311
81 1.514
82 0.414
83 0.347
84 2.682
85 10.070
86 2.362
87 6.891
88 2.625
89 1.079
90 2.864
91 0.142
92 1.254
93 0.330
94 0.431
95 4.820
96 4.098
97 6.101
98 5.278
99 0.768
100 0.966
101 0.993
102 2.849
103 1.008
104 1.509
105 2.558
106 3.516
107 2.183
108 5.345
109 0.058
110 6.516
111 0.916
112 1.568
113 0.862
114 3.710
115 0.144
116 1.721
117 2.678
118 9.186
119 1.962
120 0.234
121 0.809
122 0.874
123 1.339
124 0.003
125 2.163
126 1.514
127 0.161
128 3.060
129 0.998
130 7.047
131 4.248
132 2.060
133 1.581
134 0.947
135 6.386
136 5.013
137 0.425
138 11.361
139 2.464
140 1.191
141 2.251
142 0.878
143 7.162
144 2.293
145 5.046
146 5.380
147 5.345
148 0.809
149 0.815
150 2.406
151 0.797
152 1.246
153 0.626
154 2.141
155 1.678
156 2.389
157 3.108
158 1.070
159 2.447
160 4.763
161 1.082
162 0.524
163 0.317
164 4.896
165 0.831
166 2.649
167 0.324
168 1.071
169 4.768
170 2.534
171 4.018
172 1.671
173 2.370
174 0.883
175 2.965
176 2.145
177 2.002
178 4.583
179 0.606
180 0.906
181 0.948
182 1.372
183 0.576
184 6.386
185 4.168
186 0.579
187 1.714
188 2.676
189 1.818
190 0.208
191 0.645
192 0.899
193 0.168
194 10.641
195 1.947
196 2.712
197 0.738
198 0.389
199 0.538
200 12.829
201 2.228
202 18.299
203 0.519
204 4.247
205 0.758
206 0.774
207 0.694
208 0.127
209 0.007
210 2.558
211 3.307
212 8.520
213 4.597
214 0.453
215 0.653
216 6.452
217 0.810
218 2.791
219 1.874
220 3.646
221 0.305
222 0.614
223 1.972
224 2.963
225 0.565
226 7.966
227 0.921
228 0.399
229 3.768
230 1.921
231 1.867
232 0.713
233 0.203
234 0.280
235 1.126
236 2.345
237 0.320
238 2.451
239 1.332
240 1.616
241 0.245
242 0.143
243 0.130
244 7.927
245 1.159
246 1.239
247 2.596
248 8.418
249 5.140
250 2.552
251 2.599
252 2.272
253 0.688
254 1.507
255 0.306
256 2.696
257 0.787
258 2.536
259 3.630
260 0.347
261 3.529
262 1.199
263 2.124
264 1.612
265 2.740
266 2.858
267 4.201
268 5.368
269 0.788
270 0.701
271 3.645
272 1.454
273 2.560
274 0.504
275 4.635
276 6.288
277 0.043
278 1.570
279 0.217
280 0.906
281 1.003
282 0.581
283 1.268
284 1.384
285 1.877
286 1.065
287 0.297
288 2.647
289 8.310
290 7.065
291 0.168
292 0.734
293 0.025
294 2.619
295 0.816
296 6.008
297 0.071
298 0.323
299 3.960
300 0.011

check values

1.a. Sample #2 sample mean = 8.5
2. UCL = 0.50
3.
4. Z = -2.17
5.a. mean = 2.532
5.b. Obs #2, Z = -0.706