Using the table of the Chi-square distribution, if X is 2 (5), determine the con
ID: 3291622 • Letter: U
Question
Using the table of the Chi-square distribution, if X is 2(5), determine the constants c and d so that P(c < X < d) = 0.90 and P(X < c) = 0.005.
673 Tables of Distributions Table II Chi-square Distribution The following table presente selected quantiles of chi-square distributiong Le, the values a such that for selected degrees of freedom r. r 0.010 0.025 0.050 0.100 0.900 0.950 0.97 0.900 20.020 0.051 0.103 0.21 4.605 .991 7.37 9.210 30.115 0.2160352 0.584 6.251 7.815 9.348 11.345 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 60.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 1.230 1.690 2.167 2.833 12.017 14.067 16.013 18.476 8 1.646 2.180 2.733 3.40 13.362 15.607 17.535 20.090 92.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 10 2.558 3.247 3.940 4.865 15.087 18.307 20.483 23.200 11|3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 12 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 134.107 6.009 .82 7.042 19.812 22.362 24.736 27.688 144.600 5.629 6.571 7.700 21.064 23.685 26,119 29.141 155.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 16 6.812 6.908 7.962 9.312 23.542 26.206 28.845 32.000 17 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.400 18 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.80 10 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 208.260 9.501 10.851 12.443 28.412 31.410 34.170 37.566 21 8.807 10.283 11.591. 13.240 29.615 32.671 35.479 38.932 229.542. 10.982 12.338 14.041 30.813 33.924 36.781 40.289 23 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 2410.856 12.401 13.848 15.650 33.196 36.415 39.364. 42.08 25 11524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 26 12.198 13.844 15.370 17.292 35.563 38.885 41.923 45.642 27 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 28 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 20 14.256 16.047 17.708 10.768 39.087 42.557 45.722 49.588 30 14.953 16.791 18.493 20.59 40.256 43.77S 46.979 50.892Explanation / Answer
From the table,
We can see the row for r = 5 because the degrees of freedom is 5 here. Given that:
P(X < 1.145) = 0.05
Hence,
C = 1.145
Also,
P(c < X < d) = 0.90
P(X < d) - P(X < c) = 0.90
P(X < d) - 0.05 = 0.90
P(X < d) = 0.95
From the table,
P(X < 11.070) = 0.95
Therefore,
c = 1.145
d = 11.070
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