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t yot wered nts out of A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 511 and a standard deviation of 60. A local Junior High principal has decided to give an award to any student who scores in the top 10% of statewide scores. How high should a student score be to win this award? Flag Give your answer to the nearest integer. For help on how to input a numeric answer, please see the instructions for entering numeric
math   Statistics-And-Probability   
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Answer #1

Since the distribution is normal hence, Z statistic will be in use here .

Too 10 % says top p value ,or 0.01 value in the Z table shown below.

The table suggest Z score for top 0.1 area in bell shaped curve is 1.282

Hence by using Z statistic formula

X-511 60 → 1.282 → X = 587.92

So at least they should score 588

Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive 7-scores 3.4 0.0003 0,0003 0.0003 0.0003 ,0003 0.0003 00003 0.0003 0.0003 0.0002 ฐี.Ol 0.0013 0.0013 ú.DCDI 3 0.0012 0.0012 ข.001 1 000 1 1 0.0011 0.0010 D.C. -2.9 0.0019 0.0018 0.0018 00017 0,0016 0.0016 00015 0.0015 0.001 0.0014 0.0026 0.D05 .04 0.023 OD23 0.0022 0002 002 D.0020 D.019 2.7 0.0035 0.003 0.0033 0.032 0.003 0.0030 00029 00028 00027 0.0026 26 0.007 0.0015 0.0011 0.0013 0,00 0.0010 00039 0.0038 0.0037 0.0036 0.6179 0.6217 0.6255 0.6193 06331 D6368 0540 D6443 0.6480 0.6517 0.6554 0.6591 0.6628 0.6664 06700 DST36 DS72 D.6808 0.6844 0.6879 0.6915 0.6950 0.6985 0.7019 0.705 0.7088 07123 0.7157 0,7190 0.7224 0.7257 0729 0.7324 0.7357 07389 07422 7454 D.7486 0.7517 0.7549 0.7580 0.711 0.7642 0.673 0.770 07734 07764 0.79 0.7823 0.7852 0.7881 0.7910 0.7939 0.97 0.7995 08023 8051 08078 0.8106 0.8133 O.8 i 59 0.$186 0.S212 0.823民 0.8264 D.S289 083 15 D.S340 D.8365 0.8389 0.8413 0.8438 0816 08485 .8508 083 8554 D577 0.8599 0.8621 0.5 -2.4 0.0082 0.0080 0.0078 0.0075 0003 0.00 000S9 0.0068 0.0066 0.0064 23 0.07 0.0104 .0102 og .0604 000 0 0.008 D.0084 -2.2 | 0.0139 0.01 36 0.0132 U.0 i 29 UL125 U.0122 001 19 0.01 16 0.01 13 DO1 10 0.0179 0.0174 0.01TO 0.0166 0.0162 0.0158 00154 00150 0.0146 0.0143 -2.0 0.0228 0.0222 ถ.ถ217 0.02 1 2 0.0207 ด.0202 OOI97 0.0192 0.0188 D.D183 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 09115 0913 0.9147 0.9162 0.9177 0.9102 ด.9207 0.9722 0.9236 0.9251 09265 D9279 D9292 0.9306 0.03เจ 1.5 0.9332 09345 0.935 0.9370 0.9382 0.9394 09406 .9418 0.9429 0.941 n9452 0.9463 0.0474 ด.9484 O9495 09505 09515 D9525 ถ9535 ถ.9545 n.9554 ด.9564 0.9573 ด.9582 Q9591 0.9599 D9606 D 9616 09625 0.9633 0.0359 0.D351 ถ.กา44 ด.0336 ด.0379 0.0 0.03 14 0.0307 0.0301 0.0204 1.7 | 0.0446 0.0476 0.0427 0.0418 0.0409 ด.0401 ao392 0.0384 0.0375 D.D367 10.0548 0.053 0.026 0.0516 0050 00493 00483 0045 0.0465 00455 -1,5 0.08 0.055 0,0543 0,0530 ,0618 0,006 00594 00582 0.057 D,0559 09713 0.97 19 0.9726 (19732 о,9738 0.9744 D9750 D9756 ถ9761 0.9767 U.9772 0.9778 0.9783 0.9788 09793 09y 098J3 D.9808 U.9812 0.9817 2.1 0.982 026 0830 0.9834 09838 09842 09846 D.9850 09854 0857 09861 ถ.9864 0.9868 ด.9871 09875 09878 09881 D9884 098R7 ถ.9890 2.3 U.9893 0.9896 0.9898 0.9901 0.9904 0g906 0gX9 D.991 l U.9g I 3 0.9g16 1.2 0,0 2 ,093 ,1075 0,056 01038 0.1020 0.1003 ,0085 -1.1 0.1357 D. 1335 U. 1314 U.1292 0.1271 ข. 1251 0.1230 0.1210 0.1190 D.1170 10 0.1587 562 0.1539 1515 0.1492 0.19 0.1446 01423 0.140 0.1379 0.1814 0. 1788 ข.1762 0.1736 ข. 1711 0.1685 01660 D.1635 D.1611 0.2119 D.2090 U.2061 υ.2033 U.2005 ข.197了 0.1949 0.1922 D.1894 D.1367 07 0.2420 0.2389 0.2358 0.2327 0,2296 0.2266 02236 0.2206 0.2177 0.2148 0.2743 0.2709 0.2676 d.2643 0.2611 ข.2578 02546 0.514 D.2483 D.245 1 2.9 0.998 0.9982 09982 0,9983 0.998 0998 09985 0.9985 0.9986 0,9986 0 0.3116 0.3409 0.3372 0.3336 0.3300 03264 03228 03192 0.3156 0.3121 0.2 04207 0.4168 0.4129 0.4090 0.4052 0.4013 03974 03936 0.3897 0.3859 al | 0.4602 0.4562 á.4522 ต.4483 O.4443 0.4404 0.4364 04325 0.4286 D.4247 Note that the probabilities given in this table represent the area to the LEFT of the z-score The area to the RIGHT of a z-score 1-the area to the LErr of the z-score

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