Question

Labrador Retrievers have long been popular dogs and again top registrations for the American Kennel Club. Weights of Labrador Retrievers have a mean of 65 pounds and standard deviation 3 pounds. We will assume Labrador Retriever weights have a Normal distribution. Instead of telling you how much your Labrador Retriever weighs, your veterinarian tells you that the z-score for your dog is 1.5. How much does your Labrador weigh

Answer 1

Answer:

Labrador weighs 69.5 lbs.

Step-by-step explanation:

Given the following data:

Mean (μ) = 65 pounds

Standard deviation (σ) = 3 pounds

z- score = 1.5

The formula for calculating the z-score is:

z = (x - μ)/σ

Where:

z = z-score

x = data point

μ = mean

σ = standard deviation

Since we're looking for the value of x, we can rearrange the formula algebraically:

z = (x - μ)/σ

(σ)z = [(x - μ)/σ] (σ)

σz = x - μ

Add μ to both sides:

σz + μ = x - μ + μ

x = σz + μ

Plug in the given values into the formula for x:

x = σz + μ

x = 3(1.5) + 65

x = 4.5 + 65

x = 69.5 pounds

Therefore, the Labrador weighs 69.5 pounds.

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