The height of 2 year old children are normally distributed with a mean of 32 inches and standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2 year old children that could be a problem. Find the probability of these events: a. A 2-year-old is taller than 36 inches. b. A 2-year-old is shorter than 34 inches. c. A 2-year-old is between 30 and 33 inches tall. NOTE: Answer the following questions stated above using the Normal Distribution Z table.(attached in the image). Compute and SHOW THE GRAPH of the answers too.
The height of 2 year old children are normally distributed with a mean of 32 inches and standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2 year old children that could be a problem. Find the probability of these events: a. A 2-year-old is taller than 36 inches. b. A 2-year-old is shorter than 34 inches. c. A 2-year-old is between 30 and 33 inches tall. NOTE: Answer the following questions stated above using the Normal Distribution Z table.(attached in the image). Compute and SHOW THE GRAPH of the answers too.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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2. The height of 2 year old children are
Find the probability of these
a. A 2-year-old is taller than 36 inches.
b. A 2-year-old is shorter than 34 inches.
c. A 2-year-old is between 30 and 33 inches tall.
NOTE: Answer the following questions stated above using the Normal Distribution Z table.(attached in the image). Compute and SHOW THE GRAPH of the answers too.
Transcribed Image Text:Areas Under the One-Tailed Standard Normal Curve
This table provides the area between
the meanand some Z score.
For example, whenz score = 1.45
0.4265
the area - 0.4265.
145
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.08
0.09
0.0
0.0199 0.0239
0.0000
0.0398
0.0040
0.0080
0.0120
0.0160
0.0279
0.0319
0.0359
0.1
0.0438
0.0478
0.0517
0.0557
0.056
0.0636
0.0987 0.1026
0.0675
0.0714
0.0753
0.0910
0.0832 0.0871
0.1217
0.0948
0.1331
0.1064
0.1443
0.2
0.0793
0.1103
0.1141
0.1255
0.1368
0.1736 0.1772
0.3
0.1480
0.1179
0.1554
0.1293
0.1406
0.1517
0.4
0.1591
0.1628
0.1664
0.1700
0.1808
0.1844
0.1879
0.5
0.1915
0.1900
0.1985
0.2019
D.2054
0.2083
0.2123
0.2157
0.2190
0.2224
0.2422 0.2454
0.2734 0.2764
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2486
0.2517
0.2549
0.2073
0.2967
0.7
0.2580
0.2611
0.2642
D.2704
0.2794
0.2823
0.2852
0.8
0.2881
0.2910
0.2939
0.2995
0.3023
0.3051
0.3078 0.3106
0.3133
0.9
0.3159
0.3180
0.3212
0.3238
0.3264
0.3289
0.3315
0.3340
0.3365
0.3389
1.0
0.3485
0.3413
0.3643
0.3438
0.3461
D.3508
0.3531
0.3554
0.3577
0.3599
0.3621
0.3708
0.3907
1.1
0.3665
0.3686
0.3729
0.3749 0.3770
0.3790
0.3810
0.3830
0.388
0.4066
1.2
0.3849
D.3869
0.3925
0.3944
0.3962
0.3980
0.3997
0.4015
1.3
0.4032
0.4049
0.4082
0.4099
0.4115
0.4131
0.4147
0.4162
0.4177
1.4
0.4192
0.4207
0.4222
0.4236
D.4251
0.4265
0.4279
0.4292
0.4306
0.4319
1.5
0.4332
0.4345
0.4357
0.4370
0.4382
0.4394
0.4406
0.4418
0.4429
0.4441
1.6
0.4452
0.4463
0.4474
0.4484
0.4495
0,4505
0.4515
0.4525
0.4535
0.4545
1.7
0.4554
0.4564
0.4573
0.4582
0.4608
0.4591
0.4671
0.4599
0.4616
0.4625
0.4633
1.3
0.4641
0.4649
0.4656
0.4664
0.4678
0.4686
0.4693
0.4699
0.4706
0.4726
0.4783
0.4830
1.9
0.4713
0.4719
0.4732
0.4738
0.4744
0.4750
0.4756
0.4761
0.4767
2.0
0.4772
0.4778
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
0.4834
0.4842 0.4846
0,4878
2.1
0.4821
0.4361
0.4826
0.4838
0.4850
0.4884
0.4854
0.4857
2.2
0.4804
0.4868
0.4871
0.4875
0.4881
0.4887
0.4890
2.3
0.4893
0.4896
0.4898
0.4901
0.4904
0.4906
0.4909
0.4911
0.4913
0.4916
0.4922
0.4925
0.4943
2.4
0.4918
0.4920
0.4927
0.4929
0.4931
0.4912
0.4934
0.4936
2.5
0.4938
0.4940
0.4941
0.4945
0.4946
0.4948
0.4949
0.4951
0.4952
2.6
0.4953
0.4965
0.4956
0.4960 0.4961
0.4957
0.4968
0.4977
0.4959
0.4962
0,4963 0.4964
2.7
0.4965
0.4966
0.4967
0.4969
0.4970
0.4971
0.4972
0.4973
0.4974
2.8
0.4974
0.4975
0.4976
0.4977
0.4978
0.4979
0.4979
0.4980
0.4981
2.9
0.4981
0.4932
0.4982
0.4983
0.4934
0.4984
0.4985
0.4985
0.4986
0.4986
3.0
0.4987
0.487
0.4987
0.4988
0.4988
0.4989 0.4989
0.4989
0.4990
0.4990
3.1
0.4990
0.4991
0.4991
0.4991
0.4992
0.4992
0.4992
0.4992
0.4993
0.4993
0.4994
0.4995
0.4993
0.4995
0.4995 0.4995
0.4996 0,4996
0.4997
3.2
0.4993
0.4994
0.4994
0.4994
0.4994
0.4996 0.4996
0.4997
3.3
0.4995
0.4995
0.4996
0.4996
0.4997
3.4
0.4997
0.4997
0.4997
0.4997
0.4997
0.4997
0.4997
0.4998
3.5
0.4998
0.4998
0.4998
0.4998
0.4998
0.4998
0.4998
0.4998
0.4998
0.4998
3.6
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
3.7
0.4999
0.4999
0.4999
0.4999
0.4999
0.4999 0.4999
3.8
0.4999
0.4999
0.4999
0.4999
0.4999
0.4999
0.4999
0.4999
0.4999
3.9
0.5000 0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
0.5000
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