17. Students arrive at school at various times before the bell rings for the first class. The table shows data for 200 students. a. Sketch a frequency distribution histogram. [3] Time (min) Frequency 0-3 2 3-6 6 6-9 18 9-12 32 12-15 49 15-18 18-21 222 42 27 21-24 19 24-27 10 5 27-30 0 b. Add a frequency polygon to the histogram. c. Do the data appear to follow a normal distribution? Explain your reasoning. [2] [1] d. In what ways can you change the way the data is collected to determine a cause and effect relationship regarding the tardiness of students? [2] Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive Z-scores 0.00 0.04 -34 -33 -3.2 -3.1 -30 -2.9 -28 -2.0 -19 -15 -14 -13 -1.2 -1.1 -1.0 09 -0.7 -0.6 -05 04 -0.3 -0.2 0.00 0.00 0:03 0.0003 0.0003 0.0003 0.0003 0.0003 00005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0010 0.0009 0.0009 0.0009 0000 0.0006 0.0013 0.0013 00013 0.0012 0.0012 00011 0:0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0014 0.0014 00026 0.0025 0.0024 0.0023 0.0023 0.0002 0.0021 0.0021 0.0020 0.0019 -2.7 0.0035 0.0034 0.0033 0.0032 0:0031 0.0000 0.0009 0.0028 0.0027 0.0006 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -25 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0062 0.0051 0.0049 0.0048 -24 0.0062 0.0060 CL0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0002 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0064 -22 0.0139 00116 00132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170 0.0166 00162 00138 00154 0.0150 00146 00143 0.0228 0.0222 0.0217 0.0212 001200 0.0202 0.0197 0.0192 0.0188 0.0183 00267 00281 0.00274 0.0268 00362 0.0256 00050 0.0244 0.00239 0.0233 -1.8 0.0359 0.0351 00344 0.0336 0.0329 0.0322 0.0314 0.0307 0.01301 0.0294 -1.7 0:0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0092 0.0384 0.0375 0.0367 -16 0.0548 0.0537 00526 0.0516 0.0505 0.0495 00485 0.0475 0.0465 0:0668 0.0655 0.0643 0.0630 0:0618 0.0606 0.0604 0.0582 0.0571 0.0793 00778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0994 00681 0.0968 0.0951 0.0934 0.0918 0:0900 0.0865 0.0669 0.0853 0.0838 0.0823 0.1151 0.1131 Q1112 0.1093 0.1075 0.1056 0.1038 01020 0.1003 0.0965 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 01210 0.1190 0.1170 0.1587 0.1562 01539 0.1515 0.1492 0.1469 01446 0142) 0.1400 0.1379 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2000 0.2061 0.2033 0.2008 0.1977 0.199 0.1922 0.1994 0.1867 0.2420 0.2389 0.2358 02327 0.2296 0.2266 02236 0.2206 02177 0.2148 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 0.3065 03050 0.3015 012981 0.2946 0.2912 02877 0.2843 02810 0.2776 0.3446 0.3409 03372 0.3336 0.3300 0.3264 03228 0.3192 0.3156 03121 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3504 0.3557 0.3520 04207 04168 04129 04090 04052 04013 0.3974 0.3936 0.3897 005 0.0003 01.06 0.07 0.08 0.09 0.0003 0.0003 0.0003 00002 0.0004 0.0004 010004 0.0003 0.0006 0.0005 0.0005 0.0005 CL000 00007 0.0007 00011 0.0011 0.0010 0.0010 0.0015 2 0.0 0.00 0.5000 0.01 0.02 0.5040 0.5060 003 0.5120 01 0539 02 03 04 05 06 07 018 09 1.0 1.2 13 1.4 09192 1.5 16 1.7 0.0455 1.8 0.0550 1.9 20 21 22 2.3 24 25 26 27 1956 28 29 3.0 0.3483 3.1 03859 3.2 0.9987 0.9991 0.9994 -0.1 04902 0.4562 0.4522 04483 01444) 0.4404 04364 0.4325 0.4286 0.4247 3.3 09005 0.9995 0.04 0.05 0.06 0.07 0.08 0.5160 0.5199 05239 0.5279 0.5319 0.3359 05438 05478 0.5517 05557 05596 0.5636 0.5675 015714 0.5753 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 06103 0.6141 06179 06217 06255 06293 06331 06368 06406 06443 016480 06517 016554 06591 06628 06664 06700 06736 06772 0680 06915 06050 0695 0.0019 0.7054 0.7088 0.7123 07257 0.7291 0.7324 0.7357 07389 0.7422 07454 07517 0.7549 07580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 07823 0.7852 07881 0.7910 0.7939 0.7967 07995 08023 0.8051 0.8078 08106 08133 0.8159 0.8186 0.8212 08238 08264 0.8289 08315 08340 0.8365 0.8399 08413 0.8438 0.8461 0.8485 08506 08531 0.8554 0.8577 08509 0.80621 0.8643 0.8665 08686 0.8708 0.8729 0.8749 08770 08790 0.8810 0.8830 08849 0.8888 09907 08925 08944 02 0.8960 08007 09015 09032 09049 0.9066 09082 09115 09131 09147 09162 09177 0.9207 0.9222 0.9236 09251 0.9265 0.9279 0.9292 0.9306 0.9319 09332 09345 09357 0.9370 09382 0.9994 09406 09418 019429 09441 019452 09463 0.9474 0.9484 09495 0.9505 0.9515 0.9525 09535 0.9545 09554 0.9564 0.9573 0.9582 09501 0.9599 0.9608 0.9616 09625 0.0633 09641 09649 09656 0.9664 09671 09678 09686 0.9693 09699 0.9706 09713 0.9719 0.9726 0.9732 0973 0.9744 0.9750 0.9756 09761 0.9767 09772 09778 0.9783 0.9788 09793 0.9796 0.9903 0.9608 09812 0.9817 0.9821 09826 0.9830 0.9834 09838 0.9842 0.9846 0.9650 0.9854 0.9857 019061 1964 0.9868 09671 09675 09878 09881 0.9684 09687 0.0990 09893 09896 0.9998 0.9901 09904 0.9906 0.9909 0.9911 09913 0.9916 09918 019030 0.9922 09925 09927 0.0029 0.9931 0.9912 019034 0.0036 0.9938 09940 0.9941 09943 09945 0.9946 0.9948 0.9949 09951 0.9952 09953 0.9955 0.9956 0.9957 09959 09960 0.9961 0.9962 09963 0.9964 09965 0.9967 0.9968 0.9969 09970 0.9971 0,9972 019973 09974 09974 09975 0.9976 09977 09977 0.9978 0.9979 0.9979 09080 0.9981 019981 09942 0.9982 0.9983 0.9984 0.9984 09965 0.9985 09986 09996 09987 0.9987 0.9988 09988 0.9999 09969 09989 09990 0.9990 09900 0.999 0.9991 09992 0.9992 0.9992 0.9992 09903 0.9993 0.9993 0.9993 0.9994 09994 0.9994 09994 0.9995 0.9995 0.9995 0.09 06844 06879 0.7157 0.7486 0.7190 0.7224 0.9995 0.0006 0.0006 0.9996 0.9996 0.9996 09006 0.9997 -0.0 0.5000 0.1960 0.4920 01480 0.4840 0.4801 04761 04721 0.681 0.4641 3.4 09907 0.9997 0.9997 0.9997 019097 0.9997 0.9997 0.9997 09007 0.9996