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HW Quiz Chapter 12Score: 4/20 1/5 answeredQuestion 3<>The weights of a certain dog breed are approximately normally distributed with a mean of u = 50 pounds, and a standarddeviation of o = 6 pounds.A dog of this breed werghs 54 pounds. What is the dog's Z-score? Round your answer to the nearest hundredth asneeded.2=A dog has a Z-score of -1.39. What is the dog's weight? Round your answer to the nearest tenth as needed.poundsA dog has a z-score of 1.39. What is the dog's weight? Round your answer to the nearest tenth as needed.poundsCheck Answer

Sagot :

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

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