According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2) (a) Suppose the random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain. A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not. OB. The response is quantitative because the number of people satisfied can be counted. OC. The response is qualitative because the number of people satisfied can be counted. OD. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not. (b) Explain why the sample proportion, p, is a random variable. What is the source of the variability? OA. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. OB. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. OC. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. ⒸD. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is no more than 5% of the population size and np(1-p) = 10.56 ≥ 10, the distribution of p is approximately normal with μ = 0.880 and 6 = 0.032. (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.91? The probability that proportion who are satisfied with the way things are going in their life exceeds 0.91 is 0.1736. (Round to four decimal places as needed.) (e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 80 or fewer people in the sample are satisfied with their lives? ▼less than ▼%. unusual because this probability The probability that 80 or fewer people in the sample are satisfied is, which (Round to four decimal places as needed.)
According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2) (a) Suppose the random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain. A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not. OB. The response is quantitative because the number of people satisfied can be counted. OC. The response is qualitative because the number of people satisfied can be counted. OD. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not. (b) Explain why the sample proportion, p, is a random variable. What is the source of the variability? OA. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. OB. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. OC. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. ⒸD. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. (c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements. Since the sample size is no more than 5% of the population size and np(1-p) = 10.56 ≥ 10, the distribution of p is approximately normal with μ = 0.880 and 6 = 0.032. (Round to three decimal places as needed.) (d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.91? The probability that proportion who are satisfied with the way things are going in their life exceeds 0.91 is 0.1736. (Round to four decimal places as needed.) (e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 80 or fewer people in the sample are satisfied with their lives? ▼less than ▼%. unusual because this probability The probability that 80 or fewer people in the sample are satisfied is, which (Round to four decimal places as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
Related questions
Question
Transcribed Image Text:Area
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Area
Standard Normal Distribution
0.00
0.01
0,02
0,03
0.04
0.05
0.06
0.07
0.08
0.09
Standard Normal Distribution
0.5319
0.5714
0.6103
0.02
0,08
0.5000
0.5398
0.5793
0.5080
0.5478
0.5871
0.6255
0.6628
0,00
0.03
0.05
0,07
0,5040
0.5438
0.5832
0.6217
0.6591
0.5120
0.5517
0,5910
0.6293
0.6664
0.5199
0.5596
0.5987
0.6368
0.6736
0.5239
0.5636
0.6026
0.6406
0.6772
0.01
0,04
0.06
0,09
0.0
0.0003
0.0005
0.0007
0.0009
0.0013
0.0003
0.0005
0.0006
0.0009
0.0013
0.0003
0.0004
0.0006
0.0008
0.0011
0.0003
0.0004
0.0005
0.0008
0.0011
0.0003
0.0004
0.0005
0.0007
0.0010
0.0002
0.0003
0.0005
0.0007
0.0010
0.1
0.2
0.3
0.4
0.5160
0.5557
0.5948
0.6331
0.6700
0.5279
0.5675
0.6064
0.6443
0.6808
0,5359
0.5753
0.6141
0.6517
0.6879
-3.4
-33
0.0003
0.0005
0.0007
0.0010
0.0013
0.0003
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0.0006
0.0009
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0.0003
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0.0003
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0.6179
0.6554
0.6480
0.6844
-3.2
-3.1
-3.0
0.6915
0.7257
0.7580
0.7881
0.8159
0,6950
0,7291
0.7611
0.7910
0.8186
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0.7454
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0.8078
0.8340
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0.7517
0.7823
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0.8365
0.7224
0.7549
0.7852
0.5
0.7054
0.7389
0.7704
0.7995
0.8264
0.6
0.0019
0.0026
0.0035
0.0047
0.0062
0.0018
0.0025
0.0034
0.0045
0.0060
0.0018
0.0024
0,0033
0.0044
0.0059
0.0017
0.0023
0.0032
0.0043
0.0057
0.0016
0.0023
0.0031
0.0041
0.0055
0.0015
0.0021
0.0029
0.0015
0.0021
0.0028
0.0038
0.0051
0.0014
0.0020
0.0027
0.0037
0.0049
0.0014
0.0019
0.0026
0.0036
0.0048
-29
-28
0.0016
0.7
0.0022
0.0030
0.0040
0.0054
0.8
08051
0.8133
-2.7
-2.6
-2.5
0.9
0.8315
0,8389
0.0039
0.0052
0.8413
0.8643
0,8849
0.9032
0.9192
0.8438
0.8665
0.8869
0.9049
0,9207
0.8461
0.8686
0.8888
0.8485
0.8708
0.8907
0.9082
0.8508
0.8729
0.8925
0.9099
0.9251
0.8531
0.8749
0.8944
0.9115
0.9265
0.8554
0.8770
0,8962
0.9131
0.9279
0.8577
0.8790
0.8980
0.9147
0.9292
0.8599
0.8810
0.8997
0.9162
0.9306
0.8621
0.8830
0.90 15
0.9177
0.9319
1.0
1.1
-2.4
-2.3
-2.2
-2.1
-2.0
0.0082
0.0107
0.0139
0.0179
0.0228
0.0080
0.0104
0.0136
0.0174
0.0222
0,0078
00102
0.0132
0.0170
0.0217
0.0075
0.0009
0.0073
0.0096
0.0125
0.0162
0.0207
0.0071
0.0094
0.0069
0.0091
0.0119
0.0154
0.0197
0.0068
0.0089
0.0066
0,0087
0.0113
0.0146
0.0188
0.0064
0.0084
1.2
1.3
0.9066
0.0129
0.0166
0.0212
0.0122
0.0158
0.0202
0.0116
0.0150
0.0192
0.0110
0.0143
0.0183
1.4
0.9222
0.9236
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1.6
1.7
1.8
1.9
0,9332
0.9452
0.9554
0.9641
0.9713
0,9345
0.9463
0.9564
0.9649
0.9719
0.9357
0.9474
0.9573
0.9382
0.9495
0.9591
0.9394
0.9505
0.9599
0.9406
0.9515
0.9608
0.9418
0.9525
0.9616
0.9693
0.9756
0.9429
0.9535
0.9625
0,9441
0.9545
0.9633
0.9370
0.0287
0.0359
0.0446
0.0548
0.0281
0.0351
0.0436
0.0537
0.0655
0.0274
0.0344
0.0427
0.0526
0.0643
0.0250
0.0314
0.0392
0.0485
0.0594
0.9484
0.9582
0.9664
0.9732
0.0268
0.0336
0.0418
0.0516
0.0630
0.0262
0.0329
0.0409
0.0256
0.0322
0.0401
0.0495
0.0606
0.0244
0.0307
0.0384
0.0475
0.0582
0.0239
0.0301
0.0375
0.0465
0.0571
0.0233
0.0294
0.0367
-1.9
-1.8
0.9656
0.9726
0.9671
0.9738
0.9678
0.9744
0.9686
0.9750
0.9699
0.9761
0.9706
0,9767
-1.7
-1.6
-1.5
0.0505
0.0618
0.0455
0.0559
2.0
2.1
2.2
2.3
2.4
0.9772
0.9821
0.9861
0.9893
0.9918
0.9778
0,9826
0.9864
0.9896
0.9920
0.9783
0.9830
0.9868
0.9898
0.9922
0.9793
0.9838
0.9875
0.9904
0.9927
0.9798
0.9842
0.9878
0.9906
0.9929
0.9803
0.9846
0.9881
0.9909
0.9931
0.9808
0.9850
0.9884
0.9911
0.9932
0.9812
0.9854
0,9887
0.9913
0.9934
0.9817
0,9857
0.9890
0.9916
0.9936
0.0668
0.9788
0.9834
-14
-1.3
-1.2
-1.1
-1.0
0.0808
0.0968
0.1151
0.1357
0.1587
0.0793
0.0951
0.1131
0.1335
0.1562
0.0778
0.0934
0.1112
0.1314
0.1539
0.0764
0.0918
0.1093
0.0749
0.0901
0.1075
0.0735
0.0885
0.1056
0.1251
0.1469
0.0721
0.0869
0.1038
0.1230
0.1446
0.0708
0.0853
0.1020
0.0694
0.0838
0.1003
0.1190
0.1401
0.0681
0.0823
0.0985
0.9871
0.9901
0.9925
0.1292
0.1515
0.1271
0.1492
0.1210
0.1423
0.1170
0.1379
0.1841
02119
0.2420
0.2743
0.3085
0.1814
0.2090
0.2389
0.2709
0.3050
0.1788
0,2061
0.2358
0.2676
0.3015
0.1736
0.2005
0.2296
0.2611
0.2946
0.1685
0.1940
0.2236
0.2546
0.2877
0.1660
0.1922
02206
02514
02843
2.5
2.6
2.7
0.9938
0.9953
0.9965
0.9074
0,9981
0.9940
0.9955
0.9966
0,9975
0.9982
0.9941
0.9956
0.9967
0.9976
0.9982
0.9943
0.9957
0.9968
0.9945
0.9959
0.9969
0.9977
0.9984
0.9946
0.9960
0.9970
0.9978
0,9984
0.9948
0.9961
0.9971
0,9979
0.9985
0.9949
0.9962
0.9972
0.9979
0.9985
0.9951
0.9963
0,9973
0,9952
0.9964
0.9974
0.1635
0.1894
0.1762
0.2033
0.2327
0.2643
0.2981
0.1711
0.1977
0.2266
0.1611
0.1867
02148
0.2451
0.2776
-0.9
-08
0.9977
0.9983
0.9080
0,9986
0.9981
0.9986
28
0.2177
0.2483
0.2810
-0.7
2.9
0.2578
0.2912
-0.6
0.9089
0,9992
0.9994
0.9996
0.9997
-0.5
3.0
0.9987
0.9987
0,9987
0.9988
0.9988
0.9992
0.9994
0,9989
0.9992
0,9994
0.9989
0.9992
0.9995
0,9990
0,9993
0,9995
0.9990
3.1
3.2
0.9993
0.9995
0.9997
0.9998
0.9990
0,9991
0,9991
0,9991
0.3446
0.3821
0.4207
0.4602
0.5000
0.3409
0.3783
04168
0.3372
0.3745
0.4129
04522
04920
0.3336
0.3707
0.4090
0.4483
0.4880
0.3300
0.3669
0.4052
0.4443
0.4840
0.3264
0.3632
0.4013
0.4404
-04
-0.3
-0.2
-0.1
-0.0
0.3228
0.3594
0.3192
0.3557
0.3156
0.3520
0.3897
0.3121
0,3483
0.3859
0,4247
0.4641
0,9993
0.9995
0.9997
0,9903
0,9994
0.9995
0.9997
0.9994
0.9995
0.9997
0.9996
0.9997
0.3974
0.3936
3.3
0.9996
0.9996
0.9996
0.9996
3.4
0.9997
0.9997
0.9997
0.9997
04562
0.4960
0.4364
0.4761
0.4325
04721
04286
0.4801
0.4681
0,00
0.01
0,02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0,00
0.01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0.09
Transcribed Image Text:According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (e) below.
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
.....
(a) Suppose the random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain.
A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
B. The response is quantitative because the number of people satisfied can be counted.
O C. The response is qualitative because the number of people satisfied can be counted.
D. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.
(b) Explain why the sample proportion, p, is a random variable. What is the source of the variability?
O A. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.
O B. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
C. The sample proportion p is a random variable because the value of p represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.
D.
The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.
(c) Describe the sampling distribution of p, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.
Since the sample size is no more than 5% of the population size and np(1 - p) = 10.56 2 10, the distribution of p is approximately normal with µa = 0.880 and on = 0.032
р
(Round to three decimal places as needed.)
(d) In the sample obtained in part (a), what is the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.91?
The probability that proportion who are satisfied with the way things are going in their life exceeds 0.91 is 0.1736
(Round to four decimal places as needed.)
(e) Using the distribution from part (c), would it be unusual for a survey of 100 people to reveal that 80 or fewer people in the sample are satisfied with their lives?
The probability that 80 or fewer people in the sample are satisfied is
which
unusual because this probability
less than
%.
(Round to four decimal places as needed.)
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