  6. A researcher develops a test for identifying intellectually gifted children. It has au= 56 and o=8.d.What percentage of children are expected to score above 60?What percentage of the scores will be below 54?b.You measure 64 children and get a sample mean of 58.28? How likely is this sample toC.relate to the originally described population using a two tail analysis with a 0.05. Wouldyour conclusion change if we did a one tail analysis with a-0.01?

Question help_outlineImage Transcriptionclose6. A researcher develops a test for identifying intellectually gifted children. It has au= 56 and o=8. d. What percentage of children are expected to score above 60? What percentage of the scores will be below 54? b. You measure 64 children and get a sample mean of 58.28? How likely is this sample to C. relate to the originally described population using a two tail analysis with a 0.05. Would your conclusion change if we did a one tail analysis with a-0.01? fullscreen
Step 1

Area under the normal curve is the sum of all probabilities of variable X. Since probability ranges from 0 to 1, the total area under the cuve is equal to 1. We can calculate the probability of finding a score/number less than X ie P(x<X)  by calculating Z score and the finding corresponding probability of that Z score using Z table.

But if we need to find probability of a score greater than X ie P(x>X) then we first calculated P(x<X) and subtract that from 1.

Step 2

Part a)

Z score computation:

Step 3

Probability corresponding to Z score of 0.5 can be read from z table as shown below.

P(X<60)=P(Z<0.5) = ... help_outlineImage Transcriptionclose00 .06 09 .01 .02 .03 04 .05 .07 .08 Z 5359 5080 5120 5160 5199 5239 5279 5319 0.0 5000 5040 5675 .5714 5753 0.1 5398 .5438 5478 .5517 5557 .5596 5636 5987 .6026 .5832 .5871 .5910 5948 6064 6103 6141 0.2 .5793 6480 6293 6443 6517 0.3 6179 6217 6255 6331 6368 6406 6736 6808 6554 6591 .6628 .6664 6700 .6772 .6844 6879 0.4 7054 7123 7157 7190 7224 0.5 6915 6950 .6985 7019 7088 7389 7517 7549 0.6 7257 7291 7324 7357 7422 .7454 7486 7704 7734 7764 .7794 7823 7852 0.7 7580 7611 7642 7673 0.8 7939 7881 7910 7967 7995 .8023 .8051 .8078 8106 .8133 8186 8212 .8238 8264 8289 8315 8340 .8365 .8389 0.9 8159 .8461 8577 .8621 1.0 .8413 8438 .8485 .8508 .8531 8554 .8599 .8686 8810 .8708 8729 .8749 8770 8790 .8830 1.1 8643 8665 .8997 .9015 1.2 .8849 .8869 .8907 .8925 8944 .8962 8888 8980 9082 9236 9049 9066 .9099 9115 9131 9147 9162 9177 1.3 9032 .9292 .9306 .9319 9192 .9207 .9222 9251 .9265 9279 1.4 0222 024E 0257 0270 0200 0204 0406 0410 0420 0411 fullscreen

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