Question
Asked Dec 5, 2019
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Find z such that 96% of the standard normal curve lies to the left of z

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Expert Answer

Step 1

The total area under the normal curve is equal to 1 and contains 100% of all  probabilities. 

Z score tells us what percentage of area is below that value of Z.  The area under the curve shaded in yellow comprises 96% of all probabilities. This means that P(Z<z) = 0.96 

From Z table, we can read the value of this z corresponding to probability of 0.96

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Step 2

To read z value from Z table, mark your probability or approximately the same value and first write the corresponding row (1.7 in this case) and then the corresponding column( 0.05 or 0.06) and add them.  This will tell us that the z value lies between 1.75 and 1.76  as shown below. 

 

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0.03 0.01 0.02 0.04 0.05 0.06 0.07 0.08 0.09 +0 53586 50000 .50399 50798 .51197 .51595 51994 .52392 52790 53188 +0.1 54776 57142 55567 55966 56360 56749 57535 53983 54380 55172 +0.2 58317 58706 59095 59483 .60642 57926 59871 .60257 .61026 .61409 +0.3 61791 .62172 .62552 62930 .63307 .63683 64058 .64431 .64803 65173 +0.4 67724 .65542 .65910 .66276 .66640 .67003 .67364 .68082 .68439 .68793 +0.5 .69847 70884 71226 69146 69497 .70194 70540 71566 71904 72240 +0.6 .72907 73565 .73891 74215 74537 74857 72575 .73237 .75175 .75490 +0.7 .76424 77035 .77337 .77637 77935 .78230 .75804 76115 .76730 .78524 +0.8 .78814 .79103 .79389 .79673 .79955 B0234 80511 80785 .81057 81327 +0.9 81859 83147 83398 81594 82121 82381 82639 .82894 „83646 83891 +1 84134 85769 84375 84614 84849 85083 85314 85543 85993 86214 +1.1 87286 88100 86433 86650 86864 87076 87493 87698 87900 88298 +1.2 88493 .89251 89796 90147 .88686 88877 89065 .89435 89617 89973 +1.3 90320 90988 91308 91774 90490 90658 90824 91149 91466 91621 +1.4 92364 92507 92785 92922 91924 92073 92220 92647 93056 93189 +1.5 93574 93822 93319 93448 93699 93943 94062 94179 94295 94408 +1.6 94520 94950 95352 94630 94738 94845 95053 95154 95254 95449 +1.7 95637 .95728 96327 .95543 95818 95907 .95994 96080 96164 .96246 +1.8 96407 97062 96485 96562 96638 96712 ,96784 96856 96926 96995 +1.9 97257 97670 97128 97193 97320 97381 97441 97500 97558 97615 +2 97778 97725 .97831 97882 97932 97982 98030 98077 .98124 98169 +2.1 98341 98382 98461 98214 98257 .98300 .98422 98500 .98537 98574 +2.2 98870 98645 98713 98745 .98778 98809 98610 .98679 98840 98899 +2.3 98928 98956 98983 99010 99036 99061 99086 99111 99134 99158 +2.4 99180 99202 99224 99286 99305 99245 99266 99324 99343 99361 +2.5 99396 99446 99520 99379 99413 99430 99461 99477 99492 99506 +2.6 .99609 99534 99547 .99560 99573 99585 .99598 99621 .99632 99643 +2.7 99674 99653 99664 99693 99702 99711 99720 99736 99683 99728 +2.8 99767 99744 99752 .99760 99774 .99781 99788 99795 .99801 99807 +2.9 99813 99856 99819 99825 99831 99836 99841 99846 99851 99861 +3 99865 99869 .99874 99878 99882 .99886 99889 99893 .99896 99900

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Step 3

To get the exact z value use Excel ...

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A 1 =NORM.S.INV(0.96) 1.75068607125217 2

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