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.

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06-05-2021
Mathematics

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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.

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adefunkeadewole adefunkeadewole · Answer 1 · 2021-05-11T20:02:36-04:00

Answer:

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

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