1. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10,000 cookies?

sketch the curve:
solution:
2. The mean life of a battery is 50 hours with a standard deviation of 6 hours. The manufacturer advertises that they will replace all batteries that last less than 38 hours. If 50,000 batteries were produced, how many would they expect to replace?
sketch the curve:

solution:
3. The monthly income of 5,000 workers at the URC plant are distributed normally. Suppose the mean monthly income is 10,250 pesos
and the standard deviation is 250.
a) 20% of workers earn more than how much per month?
sketch the curve:
solution:
b) How many workers earn less than 8500 pesos per month?
sketch the curve:
solution:
c) What percentage of the workers earn between 8500 pesos and 12,000 pesos per month?
sketch the curve:
solution:
d) 95% of workers earn less than how much per month?
sketch the curve:
solution:

e) The middle 50% of workers earn between how much?
sketch the curve:
solution:
Transcribed Image Text:This table provides the area between the mean and some Z score. For example, when Z score = 1.45 the area = 0.4265. 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 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Areas Under the One-Tailed Standard Normal Curve 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Z 0.00 0.01 0.02 0.03 0.04 0.0000 0.0040 0.0080 0.0120 0.0160 0.0398 0.0438 0.0478 0.0517 0.0557 0.0793 0.0832 0.0871 0.1179 0.1255 0.1293 0.0910 0.0948 0.1331 0.1664 0.1700 0.1217 0.1554 0.1591 0.1628 0.2054 0.2389 0.1950 0.1985 0.2291 0.2324 0.1915 0.2257 0.2580 0.2611 0.2881 0.2910 0.3159 0.3186 0.2019 0.2357 0.4998 0.4998 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.5000 0.5000 0.5000 0.4265 0.06 0.05 0.0199 0.0239 0.0596 0.0636 0.0987 0.1026 0.1064 0.1368 0.1406 0.1443 0.1736 0.1772 0.1808 0.2088 0.2422 0.2704 0.2734 0.2995 0.3264 0.2123 0.2454 0.2642 0.2673 0.2764 0.2794 0.2823 0.2939 0.2967 0.3023 0.3051 0.3078 0.3106 0.3212 0.3238 0.3289 0.3315 0.3340 0.3365 0.3389 0.3413 0.3438 0.3461 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3643 0.3665 0.3686 0.3485 0.3708 0.3729 0.3749 0.3944 0.3790 0.3810 0.3830 0.3849 0.3869 0.3770 0.3962 0.4131 0.4147 0.4162 0.3980 0.3997 0.3888 0.3907 0.3925 0.4066 0.4082 0.4099 0.4015 0.4049 0.4115 0.4177 0.4032 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 0.4554 0.4564 0.4573 0.4582 0.4608 0.4616 0.4625 0.4633 0.4591 0.4599 0.4671 0.4678 0.4641 0.4649 0.4656 0.4664 0.4686 0.4693 0.4699 0.4706 0.4713 0.4719 0.4726 0.4732 0.4738 0.4750 0.4756 0.4761 0.4772 0.4778 0.4788 0.4793 0.4821 0.4826 0.4783 0.4830 0.4834 0.4838 0.4861 0.4864 0.4868 0.4871 0.4875 0.4893 0.4896 0.4898 0.4901 0.4904 0.4918 0.4920 0.4922 0.4925 0.4927 0.4941 0.4943 0.4945 0.4744 0.4798 0.4803 0.4808 0.4812 0.4842 0.4846 0.4850 0.4854 0.4878 0.4881 0.4884 0.4887 0.4906 0.4909 0.4911 0.4913 0.4929 0.4931 0.4932 0.4934 0.4946 0.4948 0.4949 0.4951 0.4956 0.4957 0.4960 0.4961 0.4962 0.4963 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4991 0.4992 0.4992 0.4938 0.4940 0.4953 0.4955 0.4959 0.4964 0.4972 0.4973 0.4974 0.4990 0.4990 0.4991 0.4991 0.4989 0.4989 0.4990 0.4992 0.4992 0.4993 0.4994 0.4995 0.4995 0.4993 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 0.4995 0.4996 0.4997 0.4997 0.4997 0.4997 0.4998 0.4998 0.4999 0.4999 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.5000 0.5000 0.5000 0.4999 0.4999 0.4999 0.4999 0.5000 0.5000 0.5000 0.5000 0=1 μ=0 1.45 0.07 0.08 0.09 0.0279 0.0319 0.0359 0.0675 0.0714 0.0753 0.1103 0.1141 0.1480 0.1517 0.1844 0.1879 0.2157 0.2190 0.2224 0.2486 0.2517 0.2549 0.2852 0.3133 0.4767 0.4817 0.4857 0.4890 0.4916 0.4936 0.4952

Question

1. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10,000 cookies?

sketch the curve:
solution:
2. The mean life of a battery is 50 hours with a standard deviation of 6 hours. The manufacturer advertises that they will replace all batteries that last less than 38 hours. If 50,000 batteries were produced, how many would they expect to replace?
sketch the curve:

solution:
3. The monthly income of 5,000 workers at the URC plant are distributed normally. Suppose the mean monthly income is 10,250 pesos
and the standard deviation is 250.
a) 20% of workers earn more than how much per month?
sketch the curve:
solution:
b) How many workers earn less than 8500 pesos per month?
sketch the curve:
solution:
c) What percentage of the workers earn between 8500 pesos and 12,000 pesos per month?
sketch the curve:
solution:
d) 95% of workers earn less than how much per month?
sketch the curve:
solution:

e) The middle 50% of workers earn between how much?
sketch the curve:
solution:

This table provides the area between
the mean and some Z score.
For example, when Z score = 1.45
the area = 0.4265.
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
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Areas Under the One-Tailed Standard Normal Curve
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Z
0.00
0.01
0.02
0.03
0.04
0.0000 0.0040 0.0080 0.0120 0.0160
0.0398 0.0438 0.0478 0.0517 0.0557
0.0793
0.0832 0.0871
0.1179
0.1255
0.1293
0.0910 0.0948
0.1331
0.1664 0.1700
0.1217
0.1554 0.1591 0.1628
0.2054
0.2389
0.1950 0.1985
0.2291
0.2324
0.1915
0.2257
0.2580
0.2611
0.2881 0.2910
0.3159 0.3186
0.2019
0.2357
0.4998 0.4998
0.4998 0.4998
0.4999 0.4999
0.4999
0.4999 0.4999
0.4999
0.5000 0.5000 0.5000
0.4265
0.06
0.05
0.0199 0.0239
0.0596 0.0636
0.0987 0.1026 0.1064
0.1368 0.1406 0.1443
0.1736 0.1772 0.1808
0.2088
0.2422
0.2704 0.2734
0.2995
0.3264
0.2123
0.2454
0.2642
0.2673
0.2764
0.2794 0.2823
0.2939
0.2967
0.3023 0.3051 0.3078 0.3106
0.3212
0.3238
0.3289 0.3315 0.3340 0.3365 0.3389
0.3413 0.3438
0.3461
0.3508 0.3531
0.3554 0.3577
0.3599 0.3621
0.3643 0.3665 0.3686
0.3485
0.3708 0.3729 0.3749
0.3944
0.3790 0.3810 0.3830
0.3849 0.3869
0.3770
0.3962
0.4131 0.4147 0.4162
0.3980 0.3997
0.3888 0.3907 0.3925
0.4066 0.4082 0.4099
0.4015
0.4049
0.4115
0.4177
0.4032
0.4192 0.4207
0.4222
0.4236
0.4251
0.4265
0.4279
0.4292 0.4306
0.4319
0.4332 0.4345
0.4357
0.4370
0.4382
0.4394
0.4406
0.4418 0.4429
0.4441
0.4452 0.4463
0.4474
0.4484
0.4495 0.4505
0.4515 0.4525 0.4535
0.4545
0.4554 0.4564
0.4573
0.4582
0.4608 0.4616
0.4625
0.4633
0.4591 0.4599
0.4671 0.4678
0.4641 0.4649
0.4656 0.4664
0.4686 0.4693 0.4699
0.4706
0.4713 0.4719 0.4726
0.4732
0.4738
0.4750 0.4756 0.4761
0.4772 0.4778
0.4788
0.4793
0.4821 0.4826
0.4783
0.4830 0.4834 0.4838
0.4861 0.4864 0.4868 0.4871 0.4875
0.4893 0.4896 0.4898 0.4901 0.4904
0.4918 0.4920 0.4922 0.4925 0.4927
0.4941 0.4943 0.4945
0.4744
0.4798 0.4803 0.4808 0.4812
0.4842 0.4846 0.4850 0.4854
0.4878 0.4881 0.4884 0.4887
0.4906 0.4909 0.4911 0.4913
0.4929 0.4931 0.4932 0.4934
0.4946 0.4948 0.4949 0.4951
0.4956 0.4957
0.4960 0.4961 0.4962 0.4963
0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971
0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
0.4987 0.4987 0.4987 0.4988 0.4988 0.4989
0.4991 0.4992 0.4992
0.4938 0.4940
0.4953 0.4955
0.4959
0.4964
0.4972 0.4973
0.4974
0.4990
0.4990 0.4991
0.4991
0.4989 0.4989 0.4990
0.4992 0.4992 0.4993
0.4994 0.4995 0.4995
0.4993
0.4993
0.4993
0.4994
0.4994
0.4994 0.4994
0.4995
0.4995 0.4995
0.4995
0.4996
0.4997 0.4997
0.4997 0.4997
0.4998 0.4998
0.4999
0.4999
0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
0.4997 0.4997 0.4997 0.4997 0.4997 0.4998
0.4998 0.4998 0.4998 0.4998 0.4998 0.4998
0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
0.4999 0.4999 0.4999 0.4999 0.4999
0.4999 0.4999 0.4999 0.4999 0.4999
0.5000 0.5000 0.5000
0.4999
0.4999
0.4999 0.4999
0.5000 0.5000
0.5000
0.5000
0=1
μ=0 1.45
0.07
0.08
0.09
0.0279 0.0319
0.0359
0.0675 0.0714
0.0753
0.1103
0.1141
0.1480 0.1517
0.1844
0.1879
0.2157 0.2190
0.2224
0.2486 0.2517
0.2549
0.2852
0.3133
0.4767
0.4817
0.4857
0.4890
0.4916
0.4936
0.4952

Accepted Answer

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1. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10,000 cookies? sketch the curve: solution: