Question

The weights of a certain dog breed are approximately normally distributed with a mean of μ = 55 pounds, and a standard deviation of σ = 6 pounds. Fill in the indicated boxes. μ = 55 σ = 6 A dog of this breed weighs 49 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. z = A dog has a z-score of -1.09. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has a z-score of 1.09. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds

Answer 1

Answer:

(a)z=-1

(b)48.5 pounds

(c)61.5 pounds

Step-by-step explanation:

$z-score=\dfrac{x-\mu}{\sigma}$

Given:

Mean, μ = 55 pounds

Standard deviation,σ = 6 pounds.

(a)For a dog that weighs 49 pounds.

x=49 pounds

The z-score

$=\dfrac{49-55}{6}\\=\dfrac{-6}{6}\\\\=-1$

(b)When a dog has a z-score of -1.09

$-1.09=\dfrac{x-55}{6}\\x-55=-6.54\\x=55-6.54\\x=48.46 \approx 48.5 pounds (to the nearest tenth)$

The weight of a dog with a z-score of -1.09 is 48.5 pounds.

(c)When a dog has a z-score of 1.09

$1.09=\dfrac{x-55}{6}\\x-55=6.54\\x=55+6.54\\x=61.54 \approx 61.5 pounds (to the nearest tenth)$

The weight of a dog with a z-score of 1.09 is 61.5 pounds.