Final answer:
For the highest 10%, the weight corresponds to approximately 372.32 grams. For the middle 50%, the weight lies between 353.03 grams and 366.03 grams. For the highest 80%, the weight corresponds to approximately 367.56 grams. For the lowest 10%, the weight corresponds to approximately 348.32 grams.
Step-by-step explanation:
To find the weight that corresponds to each event, we need to use the concept of z-scores. The z-score tells us how many standard deviations a data point is away from the mean. We can use the z-score formula: z = (x - mean) / standard deviation.
- For the highest 10%, we need to find the z-score that corresponds to a cumulative probability of 0.9 (1 - 0.1). Using a z-table or calculator, we find that the z-score is approximately 1.28. Substituting this value into the z-score formula, we can solve for x: x = z * standard deviation + mean = 1.28 * 9 + 360 = 372.32 grams.
- For the middle 50%, we need to find the z-scores that correspond to a cumulative probability of 0.25 and 0.75. Using the z-table or calculator, we find that the z-scores are approximately -0.67 and 0.67. Substituting these values into the z-score formula, we can solve for x: x1 = -0.67 * 9 + 360 = 353.03 grams, and x2 = 0.67 * 9 + 360 = 366.03 grams. Therefore, the weight that corresponds to the middle 50% is between 353.03 grams and 366.03 grams.
- For the highest 80%, we need to find the z-score that corresponds to a cumulative probability of 0.8. Using the z-table or calculator, we find that the z-score is approximately 0.84. Substituting this value into the z-score formula, we can solve for x: x = 0.84 * 9 + 360 = 367.56 grams.
- For the lowest 10%, we need to find the z-score that corresponds to a cumulative probability of 0.1. Using the z-table or calculator, we find that the z-score is approximately -1.28. Substituting this value into the z-score formula, we can solve for x: x = -1.28 * 9 + 360 = 348.32 grams.