Answer :
Final answer:
The actual weight of an animal with a Z-score of -1.5, given a mean weight of 1152 pounds and a standard deviation of 84 pounds, is 1026 pounds.
Explanation:
Calculating Actual Weight from a Z-Score
The question asks about the actual weight of an animal given its Z-score in a normal distribution of weights. To calculate this, we use the formula: actual weight = mean + (Z-score × standard deviation). In this case, the mean weight of the angus steers is 1152 pounds, the standard deviation is 84 pounds, and the Z-score is -1.5.
Applying the formula, we get:
- Actual weight = 1152 + (-1.5 × 84)
- Actual weight = 1152 - 126
- Actual weight = 1026 pounds
Therefore, the actual weight of an animal with a Z-score of -1.5 is 1026 pounds.
