Question

The average weight of goats on a farm is 125 pounds with a standard deviation of 12 pounds. Assuming the distribution of the weights has a mound shape:

A. Approximately what percentage of goats weigh between 113 and 137 pounds?
B. About 95% of the goats will have weights that lie within what interval?
C. Approximately what percentage of goats weigh below 137 pounds?
D. The weight distribution of the goats cannot be determined with the given information.

Answer 1

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%

Step-by-step 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.