The weights of a certain dog breed are approximately normally distributed with a mean of μ = 56 pounds, and a standard deviation of σ = 6 pounds.

Question

1. A dog of this breed weighs 46 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed.
2. z=
3. A dog has a z-score of 1.2. What is the dog's weight? Round your answer to the nearest tenth as needed.
4.  pounds
5. A dog has a z-score of -1.2. What is the dog's weight? Round your answer to the nearest tenth as needed.
6.  pounds

Answer 1

The z-score is the number of standard deviations a sample is above the mean. If we let W be the weight, when the z-score is 1.2 we have (W - 56)/6 = 1.2 so that W = 63.2.

On the other hand, in the case, the z-score is -1.2 we have (W - 56)/6 = -1.2 so that W = 48.8.