252y0821 3 31 08 ECO252 QBA2 SECOND EXAM March 28 2008 Solution 33 pages Name KEY Class Hour Show your work Make Diagrams Exam is normed on 50 points Answers without reasons are not usually acceptable I 8 points Do all the following Make diagrams x N 11 13 If you are not using the supplement table make sure that I know it 54 11 0 11 z P 0 85 z 3 31 1 P 0 x 54 P 13 13 P 0 85 z 0 P 0 z 3 31 3023 4995 8018 Values are underlined on the next page For z make a diagram Draw a Normal curve with a mean at 0 Indicate zero by a vertical line Shade the area between 0 85 and 3 31 Because this is on both sides of zero we must add together the area between 0 85 and zero and the area between zero and 3 31 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 11 Indicate the mean by a vertical line Shade the area between zero and 54 This area includes the mean 11 and areas to either side of it so we add together these two areas 16 11 2 P x 16 P z P z 2 08 13 P z 0 P 2 08 z 0 5 4812 0188 For z make a diagram Draw a Normal curve with a mean at 0 Indicate zero by a vertical line Shade the area below 2 08 Because this is on one side of zero we must subtract the area between 2 08 and zero from the entire larger area below zero If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 11 Indicate the mean by a vertical line Shade the area below 16 This area does not include the mean 11 so we subtract the area between 16 and the mean from the larger area below the mean 41 11 12 11 z P 0 08 z 2 31 3 P 12 x 41 P 13 13 P 0 z 2 31 P 0 z 0 08 4896 0319 4577 For z make a diagram Draw a Normal curve with a mean at 0 Indicate zero by a vertical line Shade the area between 0 08 and 2 31 Because this is on one side of zero we subtract the area between zero and 0 08 from the larger area between zero and 2 31 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 11 Indicate the mean by a vertical line Shade the area between 12 and 41 This area does not include the mean 11 so we subtract the area between the mean and 12 from the larger area between the mean and 41 x 055 Do not try to use the t table to get this For z make a diagram Draw a Normal curve with a mean at 0 Indicate zero by a vertical line z 055 is the value of z with 5 5 of the distribution above 4 it Since 100 5 5 94 5 it is also the 94 5th percentile Since 50 of the standardized Normal distribution is below zero your diagram should show that the probability between z 055 and zero is 94 5 50 44 5 or P 0 z z 055 4450 The closest we can come to this on the standardized Normal table is P 0 z 1 60 4452 So z 055 1 60 To get from z 055 to x 055 use the formula x z which is the opposite of z x x 11 1 60 13 31 80 If you wish make a completely separate diagram for x Draw a Normal curve with a mean at 11 Show that 50 of the 1 252y0821 3 31 08 distribution is below the mean 11 If 5 5 of the distribution is above x 055 it must be above the mean and have 44 5 of the distribution between it and the mean 31 8 11 Check P x 31 8 P z P z 1 60 13 P z 0 P 0 z 1 60 5 4452 0548 TABLE 4 The Standard Normal Distribution Example P 0 z 1 21 0 3869 z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 0 0 1 0 2 0 3 0 4 0 0000 0 0398 0 0793 0 1179 0 1554 0 0040 0 0438 0 0832 0 1217 0 1591 0 0080 0 0478 0 0871 0 1255 0 1628 0 0120 0 0517 0 0910 0 1293 0 1664 0 0160 0 0557 0 0948 0 1331 0 1700 0 0199 0 0596 0 0987 0 1368 0 1736 0 0239 0 0636 0 1026 0 1406 0 1772 0 0279 0 0675 0 1064 0 1443 0 1808 0 0319 0 0714 0 1103 0 1480 0 1844 0 0359 0 0753 0 1141 0 1517 0 1879 0 5 0 6 0 7 0 8 0 9 0 1915 0 2257 0 2580 0 2881 0 3159 0 1950 0 2291 0 2611 0 2910 0 3186 0 1985 0 2324 0 2642 0 2939 0 3212 0 2019 0 2357 0 2673 0 2967 0 3238 0 2054 0 2389 0 2704 0 2995 0 3264 0 2088 0 2422 0 2734 0 3023 0 3289 0 2123 0 2454 0 2764 0 3051 0 3315 0 2157 0 2486 0 2794 0 3078 0 3340 0 2190 0 2517 0 2823 0 3106 0 3365 0 2224 0 2549 0 2852 0 3133 0 3389 1 0 1 1 1 2 1 3 1 4 0 3413 0 3643 0 3849 0 4032 0 4192 0 3438 0 3665 0 3869 0 4049 0 4207 0 3461 0 3686 0 3888 0 4066 0 4222 0 3485 0 3708 0 3907 0 4082 0 4236 0 3508 0 3729 0 3925 0 4099 0 4251 0 3531 0 3749 0 3944 0 4115 0 4265 0 3554 0 3770 0 3962 0 4131 0 4279 0 3577 0 3790 0 3980 0 4147 0 4292 0 3599 0 3810 0 3997 0 4162 0 4306 0 3621 0 3830 0 4015 0 4177 0 4319 1 5 1 6 1 7 1 8 1 9 0 4332 0 4452 0 4554 0 4641 0 4713 0 4345 0 4463 0 4564 0 4649 0 4719 0 4357 0 4474 0 4573 0 4656 0 4726 0 4370 0 4484 0 4582 0 4664 0 4732 0 4382 0 4495 0 4591 0 4671 0 4738 0 4394 0 4505 0 4599 0 4678 0 4744 0 4406 0 4515 0 4608 0 4686 0 4750 0 4418 0 4525 0 4616 0 4693 0 4756 0 4429 0 4535 0 4625 0 4699 0 4761 0 4441 0 4545 0 4633 0 4706 0 …
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