??~?(? = 7, ?^2 = 50) and ??~?(? = 5,?^2 = 24). Find a real number c such as ?(?̅−?̅ > ?) = 0.5
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BigBeachBanana
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[math]\Pr\left(\frac{\bar{X}-\bar{Y}-2}{\sqrt{13}} >c\right)=\Pr\left(Z >\frac{c-2}{\sqrt{13}}\right) =1-\Pr\left(Z \le\frac{c-2}{\sqrt{13}}\right)=0.5[/math]Using a standard normal distribution table or calculator, can you continue?
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Thank you!
BigBeachBanana
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There's a typo in post#2, here's a redo:
[math]\Pr\left(\bar{X}-\bar{Y} >c\right)= \Pr\left(\frac{\bar{X}-\bar{Y}-2}{\sqrt{13}} >\frac{c-2}{\sqrt{13}}\right) = \Pr\left(Z>\frac{c-2}{\sqrt{13}}\right)= 1-\Pr\left(Z \le\frac{c-2}{\sqrt{13}}\right)=0.5[/math]