45 packages are randomly selected from packages received by a local parcel service. The
sample has a mean weight of 18.2 pounds. The population standard deviation is known
as 3.8 pounds.
(a) What is the 95% confidence interval for the true mean weight of all packages
received by the parcel service?
(b) At least how many packages must be selected if we want to have the margin of error
no more than 0.5 pounds?
(USE INFOR BELOW TO SOLVE)
798 Appendix A Tables TABLE A5 Areas of the Standard Normal Distribution The entries in this table are the probabilities that a standard normal andom variable is between 0 and z Use this table for: the shaded area) population standard deviation case 0.0 0.08 0.09 0.0 0.07 z 0.00 0.01 0.02 0.0 0.04 .0319 .0359 .0000 .0040 .0080 .0120 160 .0199 .0239 .0279 .0753 .0398 0438 0478 0517 0557 .0596 0636 0675 .0714 .1103 1141 .0793 0832 0871 .0910 0948 0987 1026 1064 1480 1517 .117 1217 1255 1293 1331 1368 1406 1443 1700 1736 1772 1808 1844 1879 1554 1591 1628 1664 88928 82828 .1985 .2019 .2054 .2088 .2123 2157 .2190 .2224 .1915 .1950 2549 .2257 2291 2324 2357 2389 .2422 2454 2486 251 .2734 2764 2794 .2823 2852 .2580 2611 2642 2673 .2704 .296 2995 3023 3051 3078 3106 3133 .2881 .2910 293 3264 3289 .3315 3340 .3365 .3389 .3159 3186 3212 .3238 .343 .3461 .3485 .3508 3531 .3554 3577 .3599 .3621 .3413 3665 3686 .370 3729 .3749 377 3790 381 .383 .364 3925 .3944 3962 3980 .3997 .4015 .384 3869 3888 .3907 .4032 4049 4066 .408 4099 .4115 .413 4147 .416 4177 4306 4319 1.4 .4192 4207 4222 4236 4251 4265 4279 4292 .4332 434 4357 .4370 4382 .4394 4406 4418 4429 4441 1.5 1.6 .4452 4463 4474 4484 4495 450 4515 4525 4535 454 4591 .4599 4608 4616 4625 4633 1.7 .4554 4564 4573 4582 .4656 .4664 4671 .4678 .4686 4693 .469 .4706 1.8 .4641 4649 4726 4732 4738 4744 4750 1756 4761 4767 1.9 4713 4719 .4817 .4772 4778 .4783 4788 4793 .4798 .4803 4808 .4812 .4854 .485 .4821 .4826 .4830 4834 4838 4842 4846 4850 4878 4881 1884 488 4890 NCECE .4861 4864 4868 4871 4875 .4901 4904 4906 .4909 4911 .491 4916 .4893 4896 4898 4931 1932 1934 4936 .4918 1920 1922 4925 4927 4929 4940 4941 .494. 4945 4946 .4948 4949 4951 .4952 2.5 .4938 .4953 4955 4956 4957 4959 4960 4961 4962 1963 4964 2.6 2.7 .4965 4967 4968 4969 .4970 ,4971 4972 1973 4974 4966 .497 4979 4980 .4981 2.8 .4974 4975 .4976 4977 4977 4978 4985 1986 4986 2.9 .4981 1982 4983 4984 4985 498 1984 4988 4988 4989 4989 4989 .4990 .4990 3.0 .4987 .498 .4987 4991 4992 4992 .4992 4992 4993 .4993 3.1 .4990 4991 .4991 .4994 4995 4995 .4995 3.2 .4993 4993 1994 .4994 4994 4994 4996 .4996 .4997 3.3 .4995 1995 .4995 .4996 4996 4996 .4996 .4997 .4997 .4997 .4997 .4997 .4997 .4998 3.4 4997 4997 .4997 3.5 .4998 4.0 .49997 4.5 .49999 5.0 4999997 60 .499999999CONFIDENCE LEVEL: 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 Z a/2 1.645 1.7 1.75 1.81 1.88 1.96 2.05 2.17 2.33 2.576Critical Values from the t Use this table for: sample standard Distribution deviation/ calculate by yourself case o: confidence interval Values of a for one-tailed test and a/2 for two-tailed test t.100 80% :050 90% tozs 95% 010 98% oo5 99% ,001 99.8% 3.078 6.314 2.706 31.821 53.656 18.28 1.886 2.920 4.303 6.965 9.925 22.328 1.638 2.353 3.182 4.541 5.84 10.214 1.533 2.132 2.776 3.747 4.604 7.173 1.47 2.015 2.571 3.365 .032 5.894 1.440 1.943 2.447 3.143 3.707 5.20 1.415 1.895 2.365 2.998 3.499 4.785 1.397 1.860 2.306 2.896 3.355 4.50 SHAWNE 6 6. Va VAWN- 1.383 1.833 2.262 2.821 3.250 4.297 1.372 1.812 2.228 2.76 .169 4.144 1.363 1.796 2.201 2.718 3.106 4.025 1.35 1.782 2.179 2.681 3.055 3.930 1.350 1.771 2.160 2.650 3.012 3.852 1.34 1.761 2.145 2.624 2.977 3.787 1.34 1.753 2.131 2.602 2.947 3.733 1.337 1.746 2.120 2.583 2.921 3.686 1.333 1.740 2.110 2.567 2.898 5.646 1.330 1.734 2,101 2.552 2.878 3.610 1.328 1.729 2.093 2.53 2.861 3.579 1.325 1.725 2.086 2.528 2.845 3.552 1.323 1.721 2.080 2.518 2.831 3.527 1.321 1.717 2.074 2.508 2.819 3.505 1.319 1.714 2.069 2.500 2.807 3.485 1.318 1.711 2.064 2.492 2.797 .467 1.31 1.708 2.060 2.485 2.787 3.450 1.315 1.706 2.056 2.479 2.779 3.435 1.314 1.703 2.052 2.473 2.771 3.421 1.313 1.701 2.048 2.467 2.763 3.408 1.311 1.699 2.045 2.462 2.756 3.396 1.310 1.697 2.042 2.457 2.750 3.385 1.303 1.684 2.021 2.423 2.704 3.307 1.29 1.676 2.009 2.403 2.678 3.261 1.29 1.671 2.000 2.390 2.660 3.232 1.294 .667 1.994 2.381 2.648 3.211 1.29 . 664 1.990 2.374 2.639 3.195 90 1.291 1.662 1.987 2.368 2.632 3.183 100 1.290 1.660 1.984 2.364 150 2.626 .174 1.28 7 1.655 1.976 2.351 2.609 3.145 200 1.286 1.653 1.972 2.345 2.601 3.131 00 1.282 1.645 1.960 2.326 2.576 3.090
