Question

NAME: 5 pts each 10. At Ridley High School, the mean time for running the 100-yard dash is 15.1 seconds with a standard deviation of 0.8411 seconds. The times are very closely approximated by a normal curve. Find the percent of times, rounded to one deceimal place if necessary, that are: a) Less than 16 seconds (round your 2-score to 2 decimal places). b) Greater than 14.4 seconds (round your Z-score to 2 decimal places). c) Between 15.1 and 17 seconds (round your Z-score to 2 decimal places).

Answer 1

Then, 10.8411 0.8411 Let X be the time for running the foo-yard dash. Xn N(15.1, 0.8412) 9) P(x216) = P(X-15.1., 16–15.) P(Z 21.07) = 0.85769 85.8% b) P(X>1444) = P(x-15.) 14.4-15.1 P(Z >-0.83) Piz<0.83) 0.79673 79.7% 5) P(15:1<x< 17) = P(1501-15.) p(15.) – 15.) X-15.1 7-1551 PloLZ (2.26) = P(Z (2.26) - P(220) > 10.8411 0.840 0.8411 0.8411 0.8411 0.5 0.98809 0.48809 48.8%

Probabilities for the Standard Normal distribution The distribution function is denoted by (x), and the probability density function is denoted by °(x). 1 - (x) 0 (x) = { * °(t)dt = √r si e-%22 di 0 х 0(x) °(x) Þ(x) °(x) 0(x) 0.00 0.50000 0.40 0.65542 0.80 0.78814 1.20 0.88493 1.60 0.94520 0.01 0.50399 0.41 0.65910 0.81 0.79103 1.21 0.88686 1.61 0.94630 0.02 0.50798 0.42 0.66276 0.82 0.79389 1.22 0.88877 1.62 0.94738 0.03 0.51197 0.43 0.66640 0.83 0.79673 1.23 0.89065 1.63 0.94845 0.04 0.51595 0.44 0.67003 0.84 0.79955 1.24 0.89251 1.64 0.94950 0.05 0.51994 0.45 0.67364 0.85 0.80234 1.25 0.89435 1.65 0.95053 0.06 0.52392 0.46 0.67724 0.36 0.80511 1.26 0.89617 1.66 0.95154 0.07 0.52790 0.47 0.68082 0.87 0.80785 1.27 0.89796 1.67 0.95254 0.08 0.53188 0.48 0.68439 0.38 0.81057 1.28 0.89973 1.68 0.95352 0.09 0.53586 0.49 0.68793 0.89 0.81327 1.29 0.90147 1.69 0.95449 0.10 0.53983 0.50 0.69 146 0.90 0.81594 1.30 0.90320 1.70 0.95543 0.11 0.54380 0.51 0.69497 0.91 0.81859 1.31 0.90490 1.71 0.95637 0.12 0.54776 0.52 0.69847 0.92 0.82121 1.32 0.90658 1.72 0.95728 0.13 0.55172 0.53 0.70194 0.93 0.82381 1.33 0.90824 1.73 0.95818 0.14 0.55567 0.54 0.70540 0.940.82639 1.34 0.90988 1.74 0.95907 0.15 0.55962 0.55 0.70884 0.95 0.82894 1.35 0.91149 1.75 0.95994 0.16 0.56356 0.56 0.71226 0.96 0.83147 1.36 0.91309 1.76 0.96080 0.17 0.56749 0.57 0.71566 0.97 0.83398 1.37 0.91466 1.77 0.96164 0.18 0.57142 0.58 0.71904 0.98 0.83646 1.38 0.91621 1.78 0.96246 0.19 0.57535 0.59 0.72240 0.99 0.83891 1.39 0.91774 1.79 0.96327 0.20 0.57926 0.60 0.72575 1.00 0.84134 1.40 0.91924 1.80 0.96407 0.21 0.58317 0.61 0.72907 1.01 0.84375 1.41 0.92073 1.81 0.96485 0.22 0.58706 0.62 0.73237 1.02 0.84614 1.42 0.92220 1.82 0.96562 0.23 0.59095 0.63 0.73565 1.03 0.84849 1.43 0.92364 1.83 0.96638 0.24 0.59483 0.64 0.73891 1.04 0.85083 1.44 0.92507 1.84 0.96712 0.25 0.59871 0.65 0.74215 1.05 0.85314 1.45 0.92647 1.85 0.96784 0.26 0.60257 0.66 0.74537 1.06 0.85543 1.46 0.92785 1.86 0.96856 0.27 0.60642 0.67 0.74857 1.07 0.85769 1.47 0.92922 1.87 0.96926 0.28 0.61026 0.68 0.75175 1.08 0.85993 1.48 0.93056 1.88 0.96995 0.29 0.61409 0.69 0.75490 1.09 0.86214 1.490.93189 1.89 0.97062 0.30 0.61791 0.70 0.75804 1.10 0.86433 1.50 0.93319 1.90 0.97128 0.31 0.62172 0.71 0.76115 1.11 0.86650 1.51 0.93448 1.91 0.97193 0.32 0.62552 0.72 0.76424 1.12 0.86864 1.52 0.93574 1.92 0.97257 0.33 0.62930 0.73 0.76730 1.13 0.87076 1.53 0.93699 1.93 0.97320 0.34 0.63307 0.74 0.77035 1.14 0.87286 1.54 0.93822 1.94 0.97381 0.35 0.63683 0.75 0.77337 1.15 0.87493 1.55 0.93943 1.95 0.97441 0.36 0.64058 0.76 0.77637 1.16 0.87698 1.56 0.94062 1.96 0.97500 0.37 0.64431 0.77 0.77935 1.17 0.87900 1.57 0.94179 1.97 0.97558 0.38 0.64803 0.78 0.78230 1.18 0.88100 1.58 0.94295 1.98 0.97615 0.39 0.65173 0.79 0.78524 1.19 0.88298 1.59 0.94408 1.99 0.97670 0.40 0.65542 0.80 0.78814 1.20 0.88493 1.60 0.94520 2.00 0.97725

Probabilities for the Standard Normal distribution Σ 3.71 2.11 4.12 Φ(0) Φ(0) x Φ(x) X Φ(x) Φ(x) Φ(x) 2.00 0.97725 2.40 0.99180 2.30 0.99744 3.20 0.99931 3.60 0.99984 4.00 0.99997 2.01 0.97778 2.41 0.99202 2.81 0.99752 3.21 0.99934 3.61 0.99985 4.01 0.99997 2.02 0.97831 2.42 0.99224 2.82 0.99760 3.22 0.99936 3.62 0.99985 4.02 0.99997 2.03 0.97882 2.43 0.99245 2.83 0.99767 3.23 0.99938 3.63 0.99986 4.03 0.99997 2.04 0.97932 2.44 0.99266 2.84 0.99774 3.24 0.99940 3.64 0.99986 4.04 0.99997 2.05 0.97982 2.45 0.99286 2.85 0.99781 3.25 0.99942 3.65 0.99987 4.05 0.99997 2.06 0.98030 2.46 0.99305 2.86 0.99788 3.26 0.99944 3.66 0.99987 4.06 0.99998 2.07 0.98077 2.47 0.99324 2.87 0.99795 3.27 0.99946 3.67 0.99988 4.07 0.99998 2.08 0.98124 2.48 Ο.99343 2.33 0.99801 3.28 0.99948 3.68 0.99988 4.08 0.99998 2.09 0.98169 2.49 0.99361 2.89 0.99807 3.29 0.99950 3.69 0.99989 4.09 0.99998 2.10 0.98214 2.50 0.99379 2.90 0.99813 3.30 0.99952 3.70 0.99989 4.10 0.99998 0.98257 2.51 0.99396 2.91 0.99819 3.31 0.99953 0.99990 4.11 0.99998 2.12 0.98300 2.52 0.99413 2.92 0.99825 3.32 0.99955 3.72 0.99990 0.99998 2.13 0.98341 2.53 0.99430 2.93 0.99831 3.33 0.99957 3.73 0.99990 4.13 0.99998 2.14 0.98382 2.54 0.99446 2.94 0.99836 3.34 0.99958 3.74 0.99991 4.14 0.99998 2.15 0.98422 2.55 0.99461 2.95 0.99841 3.35 0.99960 3.75 0.99991 4.15 0.99998 2.16 0.98461 2.56 0.99477 2.96 0.99846 3.36. 0.99961 3.76 0.99992 4.16 0.99998 2.17 0.98500 2.57 0.99492 2.97 0.99851 3.37 0.99962 3.77 0.99992 4.17 0.99998 2.18 0.98537 2.58 0.99506 2.93 0.99856 3.38 0.99964 3.78 0.99992 4.18 0.99999 2.19 0.98574 2.59 0.99520 2.99 0.99861 3.39 0.99965 3.79 0.99992 4.19 0.99999 2.20 0.98610 2.60 0.99534 3.00 0.99865 3.40 0.99966 3.80 0.99993 4.20 0.99999 2.21 0.98645 2.61 0.99547 3.01 0.99869 3.41 0.99968 3.81 0.99993 4.21 0.99999 2.22 0.98679 2.62 0.99560 3.02 0.99874 3.42 0.99969 3.82 0.99993 4.22 0.99999 2.23 0.98713 2.63 0.99573 3.03 0.99878 3.43 0.99970 3.83 0.99994 4.23 0.99999 2.24 0.98745 2.64 0.99585 3.04 0.99882 3.44 0.99971 3.84 0.99994 4.24 0.99999 2.25 0.98778 2.65 0.99598 3.05 0.99886 3.45 0.99972 3.85 0.99994 4.25 0.99999 2.26 0.98809 2.66 0.99609 3.06 0.99889 3.46 0.99973 3.86 0.99994 4.26 0.99999 2.27 0.98840 2.67 0.99621 3.07 0.99893 3.47 0.99974 3.87 0.99995 4.27 0.99999 2.28 0.98870 2.68 0.99632 3.08 0.99896 3.48 0.99975 3.88 0.99995 4.28 2.29. 0.98899 0.99999 2.69 0.99643 3.09 0.99900 3.49 0.99976 3.89 0.99995 4.29 0.99999 2.30 0.98928 2.70 0.99653 3.10 0.99903 3.50 0.99977 3.90 0.99995 2.31 0.98956 4.30 0.99999 2.71 0.99664 3.11 0.99906 3.51 0.99978 3.91 0.99995 2.32 0.98983 4.31 0.99999 2.72 0.99674 3.12 0.99910 3.52 0.99978 3.92 2.33 0.99010 0.99996 0.99683 2.73 4.32 0.99999 3.13 0.99913 3.53 0.99979 3.93 0.99996 2.34 0.99036 4.33 0.99999 2.74 0.99693 3.14 0.99916 3.54 0.99980 3.94 0.99996 4.34 0.99999 2.35 0.99061 2.75 0.99702 3.15 0.99918 3.55 0.99981 3.95 0.99996 2.36 0.99086 2.76 0.99711 3.16 0.99921 3.56 4.35 0.99999 0.99981 0.99111 2.17 0.99720 3.17 0.99924 2.37 3.96 0.99996 4.36 0.99999 3.57 0.99982 2.38 0.99134 2.78 0.99728 3.18 0.99926 3.97 0.99996 4.37 0.99999 3.58 0.99983 3.98 2.39 0.99158 2.79 0.99997 4.38 0.99736 0.99999 3.19 0.99929 3.59 0.99983 3.99 0.99997 4.39 0.99999 2.40 0.99180 2.80 0.99744 3.20 0.99931 3.60 0.99984 4.00 0.99997 4.40 0.99999