1) If the distribution of the weigths is normally distributed with mean = 50 pounds and std. deviation = 6 pounds, we can calculate the Z-score for a dog weigthing 54 pounds as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{54-50}{6}=\dfrac{4}{6}=0.67[/tex]2) If the Z-score is z=-1.39, we can calculate the weight as:
[tex]X_{}=\mu+z_{\cdot}\sigma=50+(-1.39)\cdot6=50-8.34=41.66[/tex]3) If the Z-score is now z=1.39, the weight is:
[tex]X_{}=\mu+z_{\cdot}\sigma=50+1.39\cdot6=50+8.34=58.34[/tex]Answer:
1) z = 0.67
2) 41.66 pounds
3) 58.34 pounds
