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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.

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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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.

 

Kindly SOLVE the problems using the Normal Distribtion Z Table (attached in the image) and SHOW THE GRAPH too, thanks.

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
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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