Answer :
The z score of a dog of this breed weighs 52 pounds is 0.571. The weight of the dog if z is -0.35 is 45.55 kg. The weight of the dog if z is 0.35 is 50.45 kg.
A z score refers to a numerical measurement that defines a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
The z score is given by:
z = (x - µ)/σ
where x is the raw score, µ is the mean, and σ is the standard deviation.
In the given case,
x = 52 pounds
µ = 48 pounds
σ = 7 pounds
Hence,
z = (52 - 48)/7 = 0.571
If z = -0.35
Then
-0.35 = (x - 48)/7
x - 48 = -2.45
x = 45.55 kg
Hence, the weight of the dog if z is -0.35 is 45.55 kg.
If z = 0.35
Then
0.35 = (x - 48)/7
x - 48 = 2.45
x = 50.45 kg
Hence, the weight of the dog if z is 0.35 is 50.45 kg.
Note: The question is incomplete. The complete question probably is: The weights of a certain dog breed are approximately normally distributed with a mean of 48 pounds, and a standard deviation of 7 pounds. A dog of this breed weighs 52 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. A dog has a z-score of -0.35. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has a z-score of 0.35. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds
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