For an educational study, a volunteer must place in the middle 50% on a test. If the mean forthe population is 100 and the standard deviation is 15, find the two limits (upper and lower) for the scores that would enable a volunteer to participate in the study 1:30 4A ? .ul ul 43Areas Under Normal...团:The entries in the table are the probabilities that a randomvariable having the standard normal distribution takes on avalue between 0 and z; they are equal to the area under thecurve shaded in the figure.AREAS UNDER THE STANDARD NORMAL CURVESecond Decimal Place in z.00.01.02.03.04.05.06.07.08.09.0.0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319.0359.0.1.0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753.1.2.0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141.2.3.1179 .1217.1255 .1293.1331 .1368 .1406 .1443.1480 .1517.3.4.1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879.4.5.1915 .1950.1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224.5.6.2257 .2291 .2324.23572389.2422 .2454 .2486 .2517.2549.6.7.2580 .2611 .2642 .2673.2704 .2734 .2764 .2794 .2823 .2852.7.8.2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078.3106 .3133.8.9.3159 .3186 3212 3238 .3264 .3289 .3315 .3340 .3365 .3389.93599 3621 1.0.3749 3770 3790 .3810 3830 1.1.3849 .3869 3888 .3907 3925 .3944 .3962 .3980 .3997 .4015 1.2.4032 .4049 4066 .4082 .4090 .4115 .4131 .4147 .4162 .4177 1.3.4192 .4207 4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.41.0.3413 .3438 .3461.3485 .3508 .3531 .3554 .35771.1.3643 .3665 .3686 .3708 37291.21.31.44441 1.5.4452 .4463 .4474 4484 .4495 .4505 .4515 .4525 .4535 .4545 1.6.4554 .4564 4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.7.4641 .4649 4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 1.8.4738 .4744 4750 .4756 4761 .4767 1.91.5.4332 .4345 4357 4370 .4382 .4394 .4406 .4418 .44291.61.71.81.9.4713 .4719 .4726 4732.4817 2.0.4854 .4857 2.1.4887 .4890 2.2.4893 .4896 4898 .4901 .4904 .4906 .4909 .4991 .4913 .4916 2.3.4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 4934 .4936 2.42.0.4772 .4778 .4783 .4788.4793 .4798 4803 .4808.48122.1.4821 .4826 .4830 .4834 .4838 .4842 .4846 .48502.2.4861 .4864 .4868 .4871 .4875 .4878 .4881 .48842.32.42.5.4938 .4940 .4941 .4943 .4945 .4946 .4948 4949 .4951 .4952 2.5.4960 .4961 .4962 .4963 .4964 2.6.4965 .4966 4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974 2.7.4981 2.8.4981 .4982 .4982 4983 .4984 .4984 4985 .4985 .4986 .4986 2.92.6.4953 .4955 4956 .4957 49592.72.8.4974 .4975 49764977 .4977 4978 4979 4979.49802.9.4990 3.0.4990 .4991 .4991 .4991 4992 .4992 .4992 .4992 .4993 .4993 3.1.4994 .4994 4994 .4995 4995 .4995 3.2.4997 3.33.43.0.4987 .4987 4987 4988 .4988.4989 4989 .4989.49903.13.2.4993 .4993 4994 .49943.3.4995 .4995 .4995 4996.4996 .4996 49964996 49963.4.4997 .4997 .4997 .4997 .4997 .4997 .4997 .49974997 4998.4998 3.5.4998 .4998 4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 3.64999 .4999 3.7.4999 3.83.5.4998 .4998 .4998 .4998 .4998.4998 .4998 4998 49983.63.7.4999 .4999 4999 4999.4999 .4999 .49993.8.4999 .4999 4999 .4999 .4999 .4999 .4999 .4999 .49993.9.50003.9For z 2 3.90, the areas are .5000 to four decimal places.

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For an educational study, a volunteer must place in the middle 50% on a test. If the mean for the population is 100 and the standard deviation is 15, find the two limits (upper and lower) for the scores that would enable a volunteer to participate in the study