Statistics Questions

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Statistics Questions

Chapter 5

Question 5.11 (Using Z Distribution Table)

Z=X-XS Z=125-10015

Z=1.667

PZ>1.67=0.9525

1 – 0.9525 = 0.0475

0.0475*100=4.75%

4.75% of the IQ scores are above Kristen’s 125.

Z=X-XS Z=82-10015

Z=-1.2

PZ<-1.2=0.1151

0.1151*100=11.51%

11.51% of the IQ scores are below 82.

Z=X-XS Z=91-10015 and 109-10015

Z=-0.6 and 0.6

P-0.6<Z=0.2743

P0.6>Z=0.7257

0.7257-0.2743= 0.4514

0.4514 *100=45.14%

45.15% of the IQ scores are within 9 points of the mean.

Z=X-XS Z=60-10015 and 140-10015

Z=-2.67 and 2.67

P-2.67<Z=0.0038

P2.67>Z=0.9962

0.9962 -0.0038= 0.9924

1- 0.9924=0.0076

0.0076 *100=0.76%

0.76% of the IQ scores are more than 40 points from the mean.

Question 5.13 (Using Z Distribution Table)

The probability closest to 0.98 is 2.06 which means the IQ score on the upper 2% is (0.98 * 15)+ 100 = 114.7

The probability closest to 0.1 is -2.32 which means the IQ score is (-2.32 * 15) + 100 = 134.8

The probability closest to 0.60 is 0.26 which means the IQ score on the upper 2% is (0.26 * 15) + 100 = 103.9

The probability closest to 0.025 is -2.81 and the probability closest to 0.975 is 2.81 which means the IQ score in the middle 95% is between (-2.81 * 15) + 100 = 57.85 and (2.81 * 15) + 100 = 142.15.

The probability closest to 0.01 is -2.33 and the probability closest to 0.99 is 2.33 which means the IQ score in the middle 99% is between -2.33*15…

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