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Answer :
Final answer:
To find the percentage of goats that weigh between 113 and 137 pounds, we need to calculate the z-scores for each weight and then find the area under the normal distribution curve between these two z-scores. The percentage is approximately 68.26%
Explanation:
To find the percentage of goats that weigh between 113 and 137 pounds, we need to calculate the z-scores for each weight and then find the area under the normal distribution curve between these two z-scores. The z-score formula is: z = (x - µ) / σ, where x is the individual weight, µ is the mean, and σ is the standard deviation.
Using the given information, the z-score for 113 pounds is (113 - 125) / 12 = -1, and the z-score for 137 pounds is (137 - 125) / 12 = 1. So we need to find the area under the curve between -1 and 1.
According to the z-table, the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. Therefore, the area between -1 and 1 is 0.8413 - 0.1587 = 0.6826, or 68.26%. So approximately 68.26% of the goats weigh between 113 and 137 pounds.
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