Question

The weights of a certain dog breed are approximately normally distributed with a mean of μμ = 56 pounds, and a standard deviation of σσ = 7 pounds.

A dog of this breed weighs 45 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 -0.53. What is the dog's weight? Round your answer to the nearest tenth as needed.

……… pounds

A dog has a z-score of 0.53. What is the dog's weight? Round your answer to the nearest tenth as needed.

           …………..pounds

Answer 1

Let define a random variable X that represent weight of a certain dog's breed.

The random variable X is normally distributed with mean 56 pounds and standard deviation 7 pounds.

A dog of this breed weighs 45 pounds. What is the dog's z-score?

Here, X=45

The z score is given by,

[ round to nearest hundredth place]

The Z score is -1.57

A dog has a z-score of -0.53. What is the dog's weight?

Here, Z=-0.53

[ round to nearest tenth place]

The weight of dog's breed is 52.3 pounds

A dog has a z-score of 0.53. What is the dog's weight?

Here, Z=0.53

[ round to nearest tenth place]

The weight of dog's breed is 59.7 pounds