A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco weighs 8 pounds. A cat’s weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the following is the best description of Gordo’s and Flaco’s weights?
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Gordo is considered unhealthy because his weight is above 2 standard deviations, which means he's already within top 5% for weight. Flaco is healthy.
To answer this question, we need to determine whether Gordo's and Flaco's weights fall within the top 5% or the bottom 5% of all cat weights.
First, let's calculate the z-scores for Gordo's and Flaco's weights, which tells us how many standard deviations they are away from the mean.
For Gordo:
z-score = (weight - mean) / standard deviation
= (15 - 9.5) / 1.5
= 3.67
For Flaco:
z-score = (weight - mean) / standard deviation
= (8 - 9.5) / 1.5
= -1
Now, we need to compare these z-scores with the z-score corresponding to the top 5% and bottom 5% of the normal distribution.
The z-score corresponding to the top 5% is 1.645 (approximately), and the z-score corresponding to the bottom 5% is -1.645 (approximately).
Since Gordo's z-score (3.67) is much higher than 1.645, his weight is located in the top 5% of all cat weights, making it classified as unhealthy.
On the other hand, Flaco's z-score (-1) is smaller than -1.645, so his weight is not located in the bottom 5% of all cat weights. Therefore, Flaco's weight is not classified as unhealthy.
In summary, Gordo's weight is classified as unhealthy, while Flaco's weight is not classified as unhealthy.
Both unhealthy
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability.
Use that to choose one of the following (that you did not include).
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