Complete Question
Miniature dachshunds, a dog breed with very short legs, run at an average speed of 13 mph with a standard deviation of 1.6 mph. Labrador retrievers run at an average speed of 22 mph with a standard deviation of 2.8 mph. Both breeds' running speeds are Normally distributed. A miniature dachshund runs down a street at 14.8 mph. It is chasing a Labrador that is running 25 mph, use their z-scores to find which dog is running faster relative to its breed
Answer:
Miniature dachshunds is faster
Step-by-step explanation:
From the question we are told that
The speed of the Miniature dachshunds is [tex]x = 14.8 \ mph[/tex]
The mean for the Miniature dachshunds is [tex]\mu_1 = 13 \ mph[/tex]
The standard deviation for the Miniature dachshunds is [tex]\sigma_1 = 1.6 \ mp h[/tex]
The speed of the Labrador is [tex]y = 25 \ mph[/tex]
The mean for the Labrador is [tex]\mu_2 = 22 \ mph[/tex]
The standard deviation for the Labrador is [tex]\sigma_2 = 2.8 \ mp h[/tex]
Generally the z-score for the Miniature dachshunds is
[tex]z_1 = \frac{x- \mu_1 }{\sigma_1}[/tex]
=> [tex]z_1 = \frac{14.8 - 13 }{1.6}[/tex]
=> [tex]z_1 = 1.125[/tex]
Generally the z-score for the Labrador is
[tex]z_2 = \frac{x- \mu_2 }{\sigma_2}[/tex]
=> [tex]z_2 = \frac{25 - 22 }{2.8}[/tex]
=> [tex]z_2 = 1.071[/tex]
From the value obtained we see that [tex]z_1 > z_2[/tex] , hence miniature dachshund is faster
