Question

Assume that women's heights are normally distributed with a mean given by u = 63.7 in, and a standard deviation given by o = 3.1 in. Complete parts a and b. a. If 1 woman is randomly selected, find the probability that her height is between 63.6 in and 64.6 in. The probability is approximately (Round to four decimal places as needed.) b. If 20 women are randomly selected, find the probability that they have a mean height between 63.6 in and 64.6 in. The probability is approximately (Round to four decimal places as needed.)

Answer 1

Given Anso Il = 63.7 in 3-1 in a) It ] women is randomly selected, Find the probability that her height is between 6 3:6 in and 64.6in (63-64 < X < 64.6) X-u We know that ZE کالا x = 63.6 ; 2= 63.6-63-7 3.) -0.03 x= 64.6 64.6 ; 2= 6466-63:7 0.29 3.) T P(636 < x264.6) = P(-0.03 < 3 <0.29) from 2- table P(-0.03 <<<0.29) = 0.0120+ 0.1141 0.1261 0.126) P(63-6 <x26406

Standard Normal Distribution Table 0 7 .00 ,01 .05 .06 .3159 .4306 0.0 0000 0398 0.2 0793 1179 0.4 .1554 0.5 .1915 0.6 .2257 0.7 .2580 0.8 .2881 0.9 1.0 .3413 1.1 .3643 1.2 .3849 1.3 4032 1.4 .4192 1.5.4332 1.6 .4452 1.7 .4554 1.8 .4641 1.9 .4713 2.0 .4772 2.1 .4821 2.2 .4861 2.3 .4893 2.4 .4918 2.5 .4938 2.6 4953 2.7 .4965 2.8 .4974 2.9 .4981 3.0 .4987 3.1 .4990 3.2 .4993 3.3 4995 3.4 .4997 3.5 .4998 .0040 .0438 .0832 .1217 .1591 .1950 .2291 .2611 2910 .3186 .3438 .3665 .3869 .4049 .4207 .4345 .4463 .4564 .4649 .4719 .4778 .4826 .4864 .4896 .4920 .4940 4955 .4966 .4975 4982 .4987 .4991 .4993 .4995 .4997 4998 .02 .03 .04 .0080 .0120 10160 .0478 20557 .0871 .0910 .0948 1255 .1293 .1331 .1628 .1664 .1700 1985 .2019 .2054 .2324 .2357 .2389 .2642 .2673 .2704 .2939 .2967 .2995 .3212 .3238.3264 3461 .3485 .3508 .3686 .3708 .3729 .3888 .3907 .3925 .4066 4082 .4099 4222 .4236 4251 .4357.4370 .4382 .4474 .4484 .4495 .4573 .4582 .4591 .4656 .4664 .4671 .4726.4732 .4738 .4783 .4788 .4793 .4830 .4834 4838 .4868 .4871 .4875 4898 .4901 .4904 .4922 .4925 .4927 .4941 .4943 .4945 .4956 .4957 4959 .4967 .4968 .4969 .4976 4977 .4977 4982 .4983 .4984 .4987 .4988 .4988 .4991 .4991 4992 .4994 .4994 .4994 4995 4996 .4996 4997 .4997 4997 .4998 .4998 4998 .0199 .0596 .0987 .1368 .1736 .2088 .2422 .2734 .3023 .3289 .3531 .3749 .3944 .4115 .4265 .4394 4505 .4599 .4678 4744 .4798 .4842 .4878 .4906 4929 .4946 4960 .4970 .4978 4984 .4989 .4992 4994 4996 .4997 .4998 .0239 .0636 .1026 .1406 .1772 .2123 .2454 .2764 .3051 .3315 .3554 .3770 .3962 .4131 .4279 .4406 .4515 .4608 .4686 .4750 .4803 .4846 .4881 .4909 .4931 .4948 .4961 .4971 .4979 .4985 .4989 .4992 .4994 4996 4997 .4998 .07 .08 .09 .0279 .0319.00 .0675 .0714 .1064 .1103 .1141 .1443 .1480 .1808 .1844 .1879 .2157 .2190 .2224 .2486 .2517 .2549 .2794 .2823 .2852 .3078 .3106 .3133 .3340 .3365 .3389 .3577 .3599 .3621 .3790 .3810 .3830 .3980 .3997 .4015 .4147 .4162 .4177 .4292 .4319 4418 .4429 .4441 .4525 .4535 .4545 .4616 .4625 .4633 4693 .4699 .4706 .4756 .4761 .4767 .4808 .4812 .4817 .4850.4854 .4857 .4884 .4887 4890 .4911 .4913 .4916 .4932 .4934 .4936 .4949 .4951 .4952 .4962 .4963 4964 4972 .4973 .4974 .4979 .4980 .4981 4985 4986 4986 .4989 .4990 .4990 4992 .4993 .4993 .4995 .4995 .4995 .4996 4996 4997 .4997 4997 .4998 4998 .4998 4998

a b) It 20 16 20 Loomen ore randomly selected, Find the probability that they have mean height between and 64-6 in 634 6 10 We know that x-all No. 63.6- 63.7 X = 63-6 , 7= 1) - 0:14 3.1 120 x = 64:6 64.6 - 63.7 Za 1.30 30) vzo P( 63,6 <x< 6406) P(-0.14 < za 1:30) from 2-table P(-0.14 Zz <1:30)= 0.0557 + 0-4032 00.4589 P(-0.142Z< 1.30) = 0.4589 P (63.6< x <64.6) 0.4589

Standard Normal Distribution Table 0 z .00 ,01 .05 .06 .07 .08 .09 00000 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0398 ,0793 .1179 .1554 1915 .2257 .2580 .2881 .3159 .3413 .3643 1.3 .4032 .4306 1.5.4332 1.6 .4452 1.7 .4554 1.8 .4641 1.9 .4713 2.0 .4772 2.1 .4821 2.2 .4861 2.3 .4893 2.4 .4918 2.5 .4938 2.6 4953 2.7 .4965 2.8 .4974 2.9 .4981 3.0 .4987 3.1 .4990 3.2 .4993 3.3 .4995 3.4 .4997 3.5 .4998 .0040 .0438 .0832 .1217 .1591 .1950 .2291 .2611 2910 .3186 .3438 .3665 .3869 .4049 .4207 .4345 .4463 .4564 .4649 .4719 .4778 .4826 .4864 .4896 .4920 .4940 .4955 .4966 .4975 4982 .4987 .4991 .4993 .4995 .4997 .4998 .02 .03 .04 .0080 .0120 .0478 .0517 .0557 .0871 .0910 1255 .1293 .1331 .1628 .1664 .1700 1985 .2019 .2054 .2324 .2357 .2389 .2642 .2673 .2704 .2939 .2967 .2995 .3212 .3238.3264 3461 .3485 .3508 .3686 .3708 .3729 .3888 .3907 .3925 .4066 4082 .4099 4222 .4236 4251 .4357.4370 .4382 .4474 .4484 .4495 .4573 .4582 .4591 .4656 .4664 .4671 .4726.4732 .4738 .4783 .4788 .4793 .4830 .4834 4838 .4868 .4871 .4875 4898 .4901 .4904 .4922 .4925 .4927 .4941 .4943 .4945 .4956 .4957 4959 .4967 .4968 .4969 .4976 4977 .4977 4982 .4983 .4984 .4987 .4988 .4988 .4991 .4991 4992 .4994 .4994 .4994 4995 .4996 .4996 .4997 .4997 4997 .4998 .4998 .4998 .0199 .0596 .0987 .1368 .1736 .2088 .2422 .2734 .3023 .3289 .3531 .3749 .3944 .4115 .4265 .4394 4505 .4599 .4678 4744 .4798 .4842 .4878 .4906 4929 .4946 4960 .4970 .4978 4984 .4989 .4992 .4994 4996 .4997 .4998 .0239 .0636 .1026 .1406 .1772 .2123 .2454 .2764 .3051 .3315 .3554 .3770 .3962 .4131 .4279 .4406 .4515 .4608 .4686 .4750 .4803 .4846 .4881 .4909 .4931 .4948 .4961 .4971 .4979 .4985 .4989 .4992 .4994 4996 4997 .4998 .0279 .0319 .0675 .0714 .1064 .1103 .1443 .1480 .1808 .1844 .2157 .2190 .2486 .2517 .2794 .2823 .3078 .3106 .3340 .3365 .3577 .3599 .3790 .3810 .3980 .3997 .4147 .4162 .4292 4418 .4429 .4525 .4535 .4616 .4625 4693 .4699 .4756 .4761 .4808 .4812 .4850.4854 .4884 .4887 .4911 .4913 .4932 .4934 .4949 .4951 .4962 .4963 4972 .4973 .4979 .4980 4985 4986 .4989 .4990 4992 .4993 .4995 .4995 .4996 4996 .4997 4997 4998 .4998 .0359 .0753 .1141 .1517 .1879 .2224 .2549 .2852 .3133 .3389 .3621 .3830 .4015 .4177 .4319 .4441 .4545 .4633 .4706 .4767 .4817 .4857 4890 .4916 .4936 .4952 4964 4974 .4981 4986 .4990 .4993 .4995 4997 .4998 4998

Hence the solution...