The weights of a certain dog breed are approximately normally distributed with a mean of $\mu=51$ pounds, and a standard deviation of $\sigma=7$ 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. \[ z=\square \text { o } \] A dog has a z-score of -0.57 . What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has a z-score of 0.57 . What is the dog's weight? Round your answer to the nearest tenth as needed. pounds

Step 1 ：The weights of a certain dog breed are approximately normally distributed with a mean of \(\mu=51\) pounds, and a standard deviation of \(\sigma=7\) pounds.

Step 2 ：A dog of this breed weighs 45 pounds. We are asked to find the dog's z-score. The z-score is a measure of how many standard deviations an element is from the mean. It is calculated by subtracting the mean from an element and then dividing the result by the standard deviation.

Step 3 ：Using the given values, we can calculate the z-score as follows: \(z = \frac{{weight - mean}}{{std\_dev}} = \frac{{45 - 51}}{{7}} = -0.8571428571428571\)

Step 4 ：Rounding to the nearest hundredth, the dog's z-score is \(\boxed{-0.86}\).

Step 5 ：A dog has a z-score of -0.57. To find the dog's weight, we can use the formula for the z-score and solve for the weight: \(weight = z \times std\_dev + mean = -0.57 \times 7 + 51\).

Step 6 ：A dog has a z-score of 0.57. To find the dog's weight, we can use the formula for the z-score and solve for the weight: \(weight = z \times std\_dev + mean = 0.57 \times 7 + 51\).