Question

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Answer 1

We have given the bottom probability ( area ) as 0.9 that is 0.9000

We find the Z score for area 0.9000

We use a Z table to find Zscore

We search for area 0.9000 inside the body of the z table

If 0.9000 area is not present inside the body of the table then we choose the nearest area tom0.9000

We get the area as 0.8997 Because it is very close to 0.9000

TABLE 5(a) continued Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .5000 .5040 5080 5120 51605199 .5239 .5279.5319.5359 0.1 .5398 5438 5478 .5517 5557 5596 .5636 .5675 .5714 .5753 0.2 .5793 .58325871 .5910 .5948 5987 .6026 .6064 6103 .6141 0.3 .6179 .6217 .6255 .6293 6331.6368 .6406 .6443 .6480 .6517 0.4 .6554 .6591 .6628 .6664.6700 .6736 .6772 .6808 .6844.6879 0.5 .6915 .6950 .6985 .7019 7054 7088 .7123 .7157 .7190.7224 0.6 .7257 7291 7324 7357 .7389.7422 .7454 .7486 .7517 .7549 0.7 .7580 .7611 7642.7673.7704 7734 .7764 .7794 .7823.7852 0.8 .7881 .7910 7939.7967 7995.8023 .8051 .8078 .8106.8133 0.9 .8159 .8186 .8212.8238 .8264 8289 .8315 .8340 .8365.8389 1.0 .8413 .8438 8461 .8485.8508 8531 .8554 .8577.8599 .8621 1.1 .8643 .8665.8686 8708 .8729.8749 .8770 .8790 8810 8830 1.2 .8849 .8869.8888 .8907.8925.8944 .8962 .8980.8997 .9015 1.3 .9032 .90499066 9082 90999115 .9131 .9147 9162 9177 1.4 .9192 .9207 9222 9236 9251 9265 .9279 .9292 9306 9319 1.5 .9332 .9345 9357 9370 93829394 .9406 9418 94299441 1.6 .9452 .9463 9474 9484 9495 9505 .9515 9525 9535 9545 1.7 .9554 .9564 9573 9582 9591 9599 .9608 .9616 9625 9633 1.8 .9641 .9649.9656 9664 9671 9678 .9686 969396999706 1.9 .9713 .9719 9726 9732 9738 9744 .9750 9756 9761 9767 .9772 .9778 9783 9788 9793 9798 .9803 9808 9812 9817 2.1 .9821 .9826 9830 9834 9838 9842 .9846 9850 9854 9857 2.2 .9861 .9864 9868 9871 9875 9878 .9881 9884 9887 9890 2.3 .9893 .9896 9898 9901 9904 9906 99099911 .9913 9916 2.4 .9918 9920 9922 9925 9927 9929 .9931 9932 9934 9936 2.5 .9938 9940 9941 9943 9945 9946 9948 99499951 9952 2.6 .9953 9955 9956 9957 995999609961 99629963 9964 2.7 .9965 9966 9967 9968 996999709971 99729973 9974 2.8 .9974 9975 9976 9977 9977 9978 .9979 .99799980 9981 2.9 9981 9982 99829983 9984 9984 .9985 .9985 9986 9986 3.0 9987 9987 9987 9988 9988 9989 .998999899990 9990 3.1 .9990 9991 9991.9991 9992.9992 .99929992 9993 9993 3.2 .9993 .9993 9994 9994 9994 9994 9994 9995 9995 9995 3.3 .9995 99959995 9996 9996 9996 .9996 .9996 9996 9997 3.4 .9997 99979997 9997 9997 9997 .9997 .9997 9997 9998 For z values greater than 3.49, use 1.000 to approximate the area. 2.0

Z score for area 0.8997 = Row headed number for 0.8997 + column headed number for 0.8997

Z score for area 0.8997 = 1.2 + 0.08 =1.28

Z score for area 0.8997 = Z score for area 0.9000 = 1.28

$\mu = mean = 100$

$\sigma=standard \ deviation = 15$

$Z \ score = \frac{x-\mu}{\sigma}$

$1.28= \frac{x-100}{15}$

$x = 19.2+100 =\boldsymbol{{\color{Purple} 119.2 }}$

Final answer:-

The indicated IQ score x is = 119.2