Question

Buster is a male Labrador Retriever who is 24.5 inches tall. The height of male Labrador Retrievers is normally distributed with a mean of 23.5 inches and a standard deviation of 0.8 inches. (The height of a dog is measured from his shoulder.) Find and interpret Buster's z-score.

Answer 1

To find Buster's z-score, use the formula z = (x - µ) / σ where x is Buster's height, µ is the mean height of male Labrador Retrievers, and σ is the standard deviation. Plugging in the values, we get z = (24.5 - 23.5) / 0.8 = 1.25. Therefore, Buster's z-score is 1.25.

Step-by-step explanation:

To find Buster's z-score, we can use the formula:

z = (x - μ) / σ

Where x is Buster's height, μ is the mean height of male Labrador Retrievers, and σ is the standard deviation.

Plugging in the values, we get:

z = (24.5 - 23.5) / 0.8 = 1.25

So, Buster's z-score is 1.25. This means that his height is 1.25 standard deviations above the mean height of male Labrador Retrievers.

Answer 2

z score = 1.25

Step-by-step explanation:

Buster is a male Labrador Retriever who is 24.5 inches tall. The height of male Labrador Retrievers is normally distributed with a mean of 23.5 inches and a standard deviation of 0.8 inches. (The height of a dog is measured from his shoulder.) Find and interpret Buster's z-score.

The formula for z-score =

z = (x-μ)/σ, where

x is the raw score = 24.5 inches

μ is the population mean = 23.5 inches

σ is the population standard deviation. = 0.8

Hence,

z = 24.5 - 23.5/0.8

z = 1.25

Probability value from Z-Table:

P(x = 24.5) = 0.89435

From the above calculation, the z-score = 1.25

The interpretation of the z score is since the z score is positive, this means the given data is higher or greater than the mean