Online HW 11: Normal Distributions Part | z = the value of interest n or T = the mean value of the distribution where o or s = the standard deviation of the distribution The registrar at Eastern University studied the grade point average (GPA's) of its students. The GPA's are normally distributed with a mean of 2.8 and a standard deviation of 0.4. Question 1 (2 points) Raj is a student at the Eastern University. She obtained a GPA of 3.8. How many standard deviation is this score above the average point? Question 2 (3 points) What percentage of students have a GPA between 2.3 and 3.87 (Write answer as percentage, rounded to 2 decimals) Question 3 (3 points) What percentage of students a have a GPA between 2.8 and 3.87 (Write answer as percentage, rounded to 2 decimals) The registrar at Eastern University studied the grade point average (GPA's) of its students. The GPA's are normally distributed with a mean of 2.8 and a standard deviation of 0.4. Question 4 (2 points) What percentage of students have a GPA of 3.8 or higher? (Write final answer as percentage, rounded to 2 decimals) Question 5 (2 points) Any student with a GPA of 3.8 or higher makes it on to the Dean's list. If 3 students are on the Dean's list, how many students are there at Eastern University? Question 6 (2 points) A student obtained a GPA of 1.0, how many standard deviation is this score below the mean? Question 7 (2 points) What percentage of students have a GPA below 1.07 C} almost 0% O 100%. Everybody does. C} almost 100% O 0%. It's impossible. Standard Normal Table: Probabilities for NEGATIVE 2-values Table values represent AREA to the LEFT of Z Z 0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 3.6 D 0002 0.0002 0.0001 0.0001 D.0001 DOOO1 0.0001 0 0001 0.0001 0.0001 -3.5 0 0002 0.0002 0.0002 0.0002 0.0002 DO002 0.0002 0 0012 0.0002 0.0002 -3.4 0 0003 0.0003 0.0003 0.0003 0.0003 DO003 0.0103 0 0003 0.0003 0.0002 -3.3 0 0005 0.0105 0.0005 0.0004 0.0004 0.0004 0.0204 0.0004 0.0004 0.0003 -3.2 0 0007 0.0107 0.0006 0.0006 0.0005 0.0005 0 0016 0.0005 0.0005 -3.1 00010 0.0109 0.0009 0.0019 0.0003 DO0OB 0.0008 0 0018 0.0007 0.0007 -3.0 00013 0.0013 0.0013 0.0012 0.0012 DO011 0.0011 0 0011 0.0010 0.0010 2.9 00019 0.0018 0.001B 0.0017 0.0016 DO016 0.0015 0:0015 0.0014 0.0014 -2.8 0 0026 0.0025 0.0024 0.0023 0.0023 DO022 0.0021 0 0021 0.0020 0.0019 -2.7 0 0035 0.003A 0.0033 0.0032 0.0031 0 0030 0.0029 0 0028 0,0027 0.0026 -2.6 D.0047 0.0045 0.0044 0.0043 0.0041 DO040 0.0039 0.0038 0.0037 0.0036 -2.5 0 0082 0.0060 0.0059 0.0057 0.0035 DO054 0.0052 0.0051 0.0049 0.004B -2.4 0 0032 0.0080 0.007B 0.0075 0.0073 0.0069 0.0058 0.0086 0.0054 -2.3 00107 0.0104 0.0102 0.0059 0.0095 0 0094 0.0091 0 0069 0.0087 0.0084 -2.2 00133 0.0136 0.0132 0.0129 0.0125 DO122 0.01 19 00116 0.0113 0.0110 -2.1 00179 0.0174 0.0170 0.0166 0.0162 DO158 0.0154 00150 0.0146 0.0143 -2.0 0 0228 0.0222 0.0217 0.0212 0.0207 DO202 0.0197 0 0192 0.0188 0.0183 -1.9 0 0237 0.0281 0.027 4 0.0258 0.0262 DO256 0.0250 0 0244 0.0239 0.0233 -1.8 0 0359 0.0351 0.0344 0.0336 0.0323 DD322 0.0314 0.0307 0.0301 0.0234 -1.7 0 0445 0.0436 0.0427 0.0418 0.0409 D0401 0.0392 0 0324 0.0375 0.0367 -1.6 0 0518 0.0537 0.0525 0.0516 0.0505 DO 195 0.0405 0.0475 0.0485 0.0155 -1.5 0 0638 0.0655 0.0643 0.0630 0.0610 DO605 0.0594 0.0562 0.0571 0.0569 -1.4 0 0808 0.0793 0.0778 0.0734 0.0749 DO735 0.0721 0 0708 0.0694 0.0631 -1.3 0 0958 0.0951 0.0934 0.0918 0.0901 0 0895 0.0869 0 0853 0.0838 0.0823 -1.2 01151 0.1131 0.1112 0.1093 0.1075 D.1056 0.1038 0 1020 0. 1003 0.0985 -1.1 0 1357 0. 1335 0.1314 0. 1252 0.1271 D.1251 0.1230 01210 0.1190 0.1 170 -1.0 0 1587 0. 1562 0.1539 0.1515 0.1492 D.1469 0.1446 0.1423 0. 1401 0.1379 -0.9 0 1841 0. 1814 0.1788 0.1762 0.1735 D.1711 0. 1685 0 1650 0. 1535 0.1611 D.8 02119 0.2090 0.2051 0.2033 0.2005 D.1977 0.1949 01922 0.1894 0.1857 0.7 02420 0.2369 0.2358 0.2327 0.2295 02256 0.2236 0 2206 0.2177 0.2148 -0.6 02743 0.2709 0.2676 0.2643 0.2611 D 2578 0.2546 0.2514 0.2483 0.2451 -0.5 0 3085 0.3090 0.2015 0.2931 0.2943 D2912 0.2377 02843 0,2810 0.2776 -0.4 03416 0.3409 0.3072 0.3036 0.3300 0.3264 0.3220 0.3192 0.3156 0.3121 -0.3 03821 0.3783 0.3745 0.3707 0.3669 D3632 0.3594 03557 0.3520 0.3483 -0.2 04207 0.4168 0.4129 0.4030 0.4052 04013 0.3574 0.3936 0.3897 0.3859 -0.1 04602 0.4562 0.4522 0.4453 0.4443 04404 0.4364 04325 0.4286 0.4247 0 5000 0.4980 0 4920 0.4890 D4801 0.4761 04721 0.4681 0,4641Standard Normal Table: Probabilities for POSITIVE z-values Table values represent AREA to the LEFT of Z 0 Z 0.00 0.01 0,02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.5000 0.5040 D.5081 0.5120 0.5160 05199 0.5238 0.5279 0.5319 0.5359 3.1 0.5396 0.5438 0.5478 0.6517 0.5567 0 5695 0.5636 0.5675 0.5714 0.5753 0.2 0.5799 0.5932 0.5971 Q.5910 0.5949 0 5967 0 4028 0.6084 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 06369 04406 0.6443 0.8480 0.8517 0.4 0.6554 0 6591 D.6829 0.6864 0.6700 0 6736 06772 0.6808 0.8344 0.6979 0.5 0.6915 0.6350 0.6383 0.7019 0.7054 07068 0.7123 0.7157 0,7150 0,7224 0.6 0.7257 0.7281 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0 7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7867 0.7905 0 8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 D.8212 0.8235 0.8264 0 8269 0.4315 0.8340 0.8365 0.8389 1.0 0.6413 0.8438 0.8461 0.8485 1.8508 0.8531 0.8654 0.6577 0.8589 0.8621 1.1 0.8643 0.6985 0.9586 0.8709 0.8729 0 9749 0 9770 0.8790 0.8810 0.8930 1.2 0.8949 0.8989 0.8989 0.8907 0.8925 0 9944 0 9962 0.8990 0.8997 0.9015 1.3 0.9032 0.9049 0.9068 0.9082 0.9069 09115 0.9131 0.9147 0.9182 0.9177 1. 0.9192 0.9207 0.9222 0.9236 1.9251 09265 0 9279 0.9202 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0 937 0.9362 0 9394 0 9408 0.9416 0.5429 0,9441 0.9452 0.9483 0.9474 0.9484 0.9495 09505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0 9584 0.9573 Q.9562 0.9591 0 9599 0 9609 0.9616 0.5625 0.9633 1.8 0.9641 0.9049 0.9856 0.9864 1.9671 09679 0 9694 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 D.9723 0.9732 0.9735 09744 0.9750 0.9758 0.9781 0.8767 2.0 0.9772 0.9778 0.9783 0.9785 0.9793 09798 0.9803 0.8608 0.8612 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9835 09842 0.9846 0.8650 0.6854 0.9857 2.2 0.9861 0.9864 D.9863 0.9871 0.9875 09878 0.9831 0.9684 0.6887 0.9530 2.3 0.9896 0.9896 0.9808 0.9801 0.9804 0.9506 0.9908 0.8911 0.6913 0.8916 2.4 0.9018 0.9920 0.9022 0.9825 0.9927 0 9529 0 9531 0.9032 0.9934 0.9036 2.5 0.9936 0.9940 0.9341 0.9543 0.9545 09949 0.9949 0.5951 0.9952 2.6 0.9953 0.9956 0.9956 0.9957 1.9969 0 9500 0.9961 0.9982 0.9983 0.9964 2.7 0.9965 0.9906 0.9967 0.9968 1.9569 09970 0 9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 1.9977 0 9979 0.9979 0.9979 0.9980 0.9481 2.9 0.9981 0.9982 0.9082 0.9583 0.9964 09564 0 9595 0.9095 0.8986 0.9086 3.0 0.9987 0.9987 0.9387 0.9585 09569 0.9939 0.8989 0.8980 0.8990 3.1 0.9980 0.899 1 D.9391 0.9891 0.9582 0.9592 0.9982 0.8092 0.5983 0.8993 3.2 0.8986 1.9953 D. 9394 0.9894 1.9584 0 9594 0.9984 0.8935 0.8955 0.8995 3.3 0.9986 0.9985 D.8395 0.9896 0.9895 0 9998 0.9098 0.5986 0.8997 3.4 0.9897 0.8997 D.9397 0.9597 1.9587 0 9597 0 9987 0.9937 0.5987 0.8398 3.0 0.9986 0.9998 0.9998 0.9805 1.9908 09508 0.9998 0.8098 0.5998 0.5958 0 9498 0.9399 0,9899 1 9559 09509 0 9895 0,5989 0,8949