The Environmental Protection Agency (EPA) is concerned about pollution caused by factories that burn sulfur-rich fuel. In order to decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger area. Assume that the mean height of chimneys in these factories is 100 meters with standard deviation 12 meters. A random sample of 40 chimney heights is obtained. a. What is the probability that sample mean height for the 40 chimneys is greater than 102 meters? b. What is the probability that sample mean height is between 101 and 103 meters? c. Find a symmetric interval about the mean, 100, such that the probability that the sample mean lies in the interval is 0.90. Normal Curve Areas .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 .0398 .0793 .0636 .1026 .1 .0438 .0478 .0517 .0557 .0596 .0675 .0714 .0753 .2 .0832 .0871 .0910 .0948 .0987 .1064 .1103 .1141 .3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517 .4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 .5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549 .7 .2580 .2611 .2642 .2673 .2704 .2734 .2764 .2794 2823 .2852 .8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 .3389 .3621 .9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 .4082 .4236 .4131 .4279 1.3 .4032 .4049 .4066 .4099 .4115 .4147 .4162 .4177 1.4 .4192 .4207 .4222 .4251 .4265 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545 1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916 .4925 .4943 .4927 .4945 .4934 .4951 .4936 .4952 2.4 .4918 .4920 .4922 .4929 .4931 .4932 2.5 .4938 .4940 .4941 .4946 .4948 .4949 N