Question
Asked Jul 5, 2019
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A normal distribution has a mean of 10 and a standard deviation of 10. What is the number such that 21% of the observations lie below it? Round your answer to the nearest tenth

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Expert Answer

Step 1

The given information is that the scores distributed normally with mean 10 and variance is 49. The standard deviation for the scores is 10. The random variable X denotes the observations. Given that the observations below the value x is 21%.

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P(X< x) 0.21 x-u x-= 0.21 P P Z< 0.21 10 х- x-10 0.21 10 x-10 (0.21) 10

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Step 2

Using Z table for finding the inverse cumulative function:

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01 02 04 os Loo03 Lo005 -34 0003 33 0005 -32 0007000 31 0010 -3.0 0013 29 0019 28 0026 270035 26 0047 25 0062 24 0082 0003 003 c000 C000 C000 003000 002 0004 0004 0005 0005 0008 0007 0004 0004 0004 06 0006 0006 0006 0008 0008 0008 0009 Lo009 0013 0013 0012 0012001100110011 0010 0010 L0018 0018 0017 0016 0016 0015 0015 0014 0014 0025 0024 0023 00230C22 0021021 00200019 LO034 0033 0045 0044 0043 00410040003900.38 0037 0036 Lo060 0059 0057 0055 00540052 loos0 0009 0032 0031 00300029 0028 0027 0026 0051 0049 004 0073 0071 0069 006 00660064 009 008 0084 01 16 0113 0110 21 0179o174 0170 0166 0162 0158 0154 0150 0146 0143 0780075 o104 o136 0096 0094 0091 23 0107 22 0139 0102 0099 0132 0129 0125 01220119 0222 0217 0212 02070202 0197 0192 0188 0183 0281 0274 02680262 0256 02500244 02390233 0351 0344 0336 0329 0322 0314 0307 0301 0294 0436 o537 20 0228 9 0287 48 0359 7 0446 04270418 0409 0401 0392 0384 0375 0367 0526 0516 0505 04904050475 046S0455 0655 o793 o951 131 1112 1093 1075 1056 1038 1020 1003 0985 1.6 0548 S 0668 14 0808 13 0968 12 J15 L1 1357 10 .1587 09 1841 08 2119 0 2420 2 0.6 2743 2709 2676 643 2611 2578 2546 2514 2463 2451 as 3053050 3015 2981 2946 2912 2877 2432810 2776 04 3446 3409 3372 3336 3300 3264 3228 3192 3156 3121 03 3821 373 3745 3707 3669 3632 3594 3557 3520 3483 02 A207 A168 4129 A090 A052 A013 3974 3936 397 3859 a 602 562 4522 3 0.0 5000 60 920 0 A40 A0 A761721 M MA 0643 0778 0934 0918 0901085 0869 0853 0838 0823 0630 06180606 0594 0582 0571 0559 0764 0749 07350721 7080694 681 314 1292 1271 1251 1230 1210 1190 1170 i562 1539 1515 1492 140 1446 1423 1401 1379 814 O9 2064 1635 1611 178 17621736 1711 1685 1660 2358 2327 2296 2266 2236 2206 2177 2148 4443 4404 A364 4325A26 A247

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Step 3

From the Z tabl...

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(0.21)-0.8 x-10081 10 x-10-0.81x10 x-10-8.1 x10-8.1 -1.9 2 The value ofx is equal to 2

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