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. (3pts) A manufacturing process outputs 2% defective items. If a sample of 10 items are selected, calculate
the following binomial probabilities.
a. P(X=1 defective)
b. P(X<=1 defective)

Prob 2

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
2. (4 pts) 65% of attendees at a sales conference are men. If you pick a random sample of 15 attendees,
a. Find the probability of exactly 7 men and 8 women being selected.
b. Find the probability of less than 9 men being selected.
c. Find the probability of no women in the sample.

Prob 3

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
3. (4 pts) Using a normal distribution having mean of 100 and standard deviation of 7.5, calculate
the followinig probabilities:
a. P(X <= 95)
b. P(X >= 110)
c. P(95 <= X <= 105)

Prob 4

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
4. (3pts) The lifetimes of certain types of car battery are normally distributed with a mean of 1258 days and
a standard deviation of 185 days. If the supplier guarantees them for 1080 days, what proportion of
batteries are expected to fail sooner than 1080 days, subject to replacement under the guarantee?

Prob 5

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
5. (4 pts) Heights of all adult males have a mean of m = 69.0 and standard deviation of s = 2.8,
in a normal distribution. Michael Jordan is 78 inches tall. But is his height exceptional
compared to the general male population?
a. Calculate the Z-score for Michael Jordan's height.
b. Interpret the meaning of the value you calculated in part a. Is Michael
Jordan's height exceptional?

Prob 6

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
6. (3 pts) A random sample of 50 students has a course averge score of 83 with a standard deviation of 6.1.
Using Excel, calculate the confidence interval half width for a 90% confidence interal of the mean score.

Prob 7

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
7. (4 pts) A tech service hot line call center is concerned about the duration of inbound calls. You have been
tasked with compiling and analyzing the center's call data, below, representing a sample of 250 calls from
a day's inbound call volume.
Customer ID Call date Call duration
125260805 10/1/10 32 a. Calculate the sample mean and standard deviation for call duration time.
125265384 10/1/10 163
125266412 10/1/10 7
125267836 10/1/10 29
125281795 10/1/10 84
125282733 10/1/10 60
125284950 10/1/10 36 b. Calculate a 95% confidence interval for the mean call duration
125286575 10/1/10 76 from the sample data.
125292230 10/1/10 85
125300266 10/1/10 52
125306688 10/1/10 39
125311602 10/1/10 101
125313493 10/1/10 194
125316250 10/1/10 283 c. Six months ago, the average call duration was 126. Based on the finding
125320565 10/1/10 173 of your confidence interval, is it reasonable to say that call duration has
125323846 10/1/10 88 not changed from 6 months ago?
125329947 10/1/10 61
125335633 10/1/10 26
125335970 10/1/10 78
125336423 10/1/10 41
125339446 10/1/10 64
125340538 10/1/10 267
125343444 10/1/10 16
125356293 10/1/10 226
125365638 10/1/10 36
125369580 10/1/10 46
125370308 10/1/10 29
125384797 10/1/10 65
125384981 10/1/10 94
125391046 10/1/10 193
125400997 10/1/10 27
126019495 10/1/10 94
126019725 10/1/10 37
126021634 10/1/10 152
126022692 10/1/10 149
126029251 10/1/10 34
126031108 10/1/10 88
126035487 10/1/10 82
126039091 10/1/10 96
126042536 10/1/10 197
126043327 10/1/10 202
126047171 10/1/10 31
126048039 10/1/10 206
126055040 10/1/10 166
126058266 10/1/10 20
126063438 10/1/10 79
126070772 10/1/10 140
126072359 10/1/10 255
126075014 10/1/10 214
126079142 10/1/10 43
126079523 10/1/10 107
126089959 10/1/10 152
126109278 10/1/10 124
126124189 10/1/10 334
126124936 10/1/10 182
126127258 10/1/10 287
127023310 10/1/10 14
127027582 10/1/10 138
127027819 10/1/10 85
127031444 10/1/10 38
127034527 10/1/10 96
127037084 10/1/10 155
127045175 10/1/10 51
127046951 10/1/10 161
127049464 10/1/10 355
127056442 10/1/10 260
127066233 10/1/10 101
127067302 10/1/10 273
127067709 10/1/10 91
127071411 10/1/10 59
127072160 10/1/10 60
127076815 10/1/10 322
127079341 10/1/10 54
127080741 10/1/10 132
127081898 10/1/10 118
127083604 10/1/10 111
127084357 10/1/10 188
127085675 10/1/10 82
127088302 10/1/10 384
127091788 10/1/10 90
127093911 10/1/10 60
127095062 10/1/10 27
127099273 10/1/10 101
127105571 10/1/10 81
128323367 10/1/10 201
128326577 10/1/10 112
128328618 10/1/10 73
128328946 10/1/10 225
128333478 10/1/10 23
128336825 10/1/10 17
128339920 10/1/10 90
128341159 10/1/10 283
128342774 10/1/10 99
128343124 10/1/10 141
128344122 10/1/10 166
128346866 10/1/10 199
128347314 10/1/10 89
128352984 10/1/10 53
128356370 10/1/10 114
128356572 10/1/10 42
128358051 10/1/10 224
128362446 10/1/10 75
128365097 10/1/10 78
128367558 10/1/10 277
128369246 10/1/10 42
128377877 10/1/10 135
128378385 10/1/10 251
128378722 10/1/10 83
128378777 10/1/10 44
128378898 10/1/10 71
128379494 10/1/10 158
128385217 10/1/10 113
128385944 10/1/10 39
128392375 10/1/10 122
128394965 10/1/10 106
128398149 10/1/10 33
128399158 10/1/10 251
128399894 10/1/10 119
128400616 10/1/10 163
128403961 10/1/10 113
128406051 10/1/10 228
128412722 10/1/10 63
128413720 10/1/10 231
128416727 10/1/10 333
128418119 10/1/10 70
128418262 10/1/10 58
128418535 10/1/10 52
128418694 10/1/10 211
128419896 10/1/10 163
128425993 10/1/10 46
128426714 10/1/10 201
128428865 10/1/10 240
128432111 10/1/10 250
128434678 10/1/10 163
128435786 10/1/10 336
128436228 10/1/10 590
128436501 10/1/10 27
128438058 10/1/10 103
128439876 10/1/10 44
128440144 10/1/10 170
128441504 10/1/10 374
128442955 10/1/10 187
128443111 10/1/10 67
128446681 10/1/10 110
128447039 10/1/10 54
128447877 10/1/10 323
128453999 10/1/10 113
128454210 10/1/10 224
128454310 10/1/10 9
128456505 10/1/10 157
128471670 10/1/10 136
128472996 10/1/10 418
128475207 10/1/10 238
128475208 10/1/10 328
128475246 10/1/10 19
128475419 10/1/10 42
128476234 10/1/10 9
128477495 10/1/10 384
128481456 10/1/10 97
128483716 10/1/10 286
128484348 10/1/10 45
128486146 10/1/10 108
128486613 10/1/10 92
128486630 10/1/10 13
129174563 10/1/10 179
129175338 10/1/10 88
129175535 10/1/10 197
129177268 10/1/10 167
129179358 10/1/10 84
129179714 10/1/10 181
129182188 10/1/10 173
129182747 10/1/10 19
129190345 10/1/10 75
129190534 10/1/10 59
129192374 10/1/10 77
129192410 10/1/10 70
129195867 10/1/10 131
129196727 10/1/10 111
129198659 10/1/10 90
129199122 10/1/10 44
129200003 10/1/10 555
129203156 10/1/10 277
129203472 10/1/10 169
129206033 10/1/10 246
129206861 10/1/10 167
129208795 10/1/10 91
129210004 10/1/10 102
129212701 10/1/10 81
129213812 10/1/10 52
129215277 10/1/10 233
129220332 10/1/10 163
129222158 10/1/10 124
129222842 10/1/10 49
129224281 10/1/10 109
129225679 10/1/10 223
129225950 10/1/10 152
129226725 10/1/10 35
129227699 10/1/10 96
129231806 10/1/10 156
129233328 10/1/10 76
129236895 10/1/10 96
129241447 10/1/10 204
129242271 10/1/10 144
129246314 10/1/10 248
129251321 10/1/10 44
129252929 10/1/10 319
129253189 10/1/10 75
129253674 10/1/10 31
129254417 10/1/10 16
129256893 10/1/10 166
129261872 10/1/10 242
129264631 10/1/10 80
129267699 10/1/10 164
129269139 10/1/10 440
129269235 10/1/10 296
129270130 10/1/10 34
129273041 10/1/10 333
129276237 10/1/10 147
129282675 10/1/10 113
129283098 10/1/10 211
129287376 10/1/10 61
129290376 10/1/10 118
129290748 10/1/10 305
129294700 10/1/10 64
129297693 10/1/10 36
129298265 10/1/10 14
129299403 10/1/10 62
129300494 10/1/10 73
129300600 10/1/10 309
129300710 10/1/10 206
129304950 10/1/10 132
129305145 10/1/10 115
129308103 10/1/10 123
129308705 10/1/10 39
129311397 10/1/10 100
129316198 10/1/10 210
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129319934 10/1/10 51
130001647 10/1/10 318
130003599 10/1/10 21
130004516 10/1/10 136
130005887 10/1/10 115
130008705 10/1/10 49
130009741 10/1/10 63
130010822 10/1/10 66
130011295 10/1/10 170
130013641 10/1/10 149
130014615 10/1/10 320
130015446 10/1/10 24
130015720 10/1/10 128

Check Values

1. a. 0.167
2. b. 0.245
3. a. 0.252
4. 16.80%
5. a. 3.21
6.
7. a. s = 100.603
b. CI half width = 12.47