6.6
| Standard Score | Quantitative Test | (63-67.2)10.3=-0.4078 |
| Standard Score | Analytical Test | (61-56.3)/6.7=0.7015 |
| Standard Score | Verbal Comprehension | (57-50.9)/3.2=1.9063 |
6.16
| a | Prop(X<10)=Prop(Z<(10-11.40)/1.8)=normalcdf(-E99,10,11.4,1.8)=0.2183 |
| b | Find x such that Prop(X,x)=Prop(Z<(x-11.4)/1.8)=0.25; invNorm(0.25,11.4,1.8)=10.1859 |
| c | Find x such that Prop(X,x)=Prop(Z<(x-11.4)/1.8)=0.95; invNorm(0.95,11.4,1.8)=14.3607 |
6.32
| a |
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| b | Proportion=10(1/30)=1/3 or 33.3% |
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6.48
| a | False |
| b | False |
| c | True |
| d | False |
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6.54
| a | Proportion(X<<750)=Proportion(Z<(750-700)/40)=Proportion(Z<1.25)=normalcdf(-E99,750,700,40)=0.89 |
| b | Proportion(Z<0.5)=normalcdf(-E99,0.5,0,1)=0.6915 |
| c | Proportion(X<x)=0.15 --> Proportion(Z<(x-700)/40)=0.15 --> x=-1.04*40+700=658.5; thus a minimum of 659; invNorm(0.15,700,40)=659. |
6.58
| a | a=Proportion(X>=34)=Proportion(Z>(34-30)/2)=Proportion(Z>=2)=normalcdf(34,E99,30,2)=0.0228 |
| b | p-value=Proportion(X>=35)=Proportion(Z>(3530)/2)=Proportion(Z>=2.5)=normalcdf(35,E99,30,2)=0.0062 |
6.78
| a | 1/7 |
| b | a=1/7, b=0.6 |
| c | p-value=(0.5)(1/7)=1/14 |
| d | (ii) increasing a |
| e | False |
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