Final answer:
To find the weight that represents the 99th percentile, use the z-score formula and substitute the given values. For the 36th percentile, follow the same steps. The third quartile represents the 75th percentile and can be found using the z-score formula.
Step-by-step explanation:
To find the weight that represents the 99th percentile, we need to find the z-score associated with the 99th percentile and then use it to find the corresponding weight. The z-score can be calculated using the formula: z = (X - mean) / standard deviation. For the 99th percentile, the z-score is approximately 2.326. Substituting this value into the formula and rearranging to solve for X, we get:
X = z * standard deviation + mean = 2.326 * 51.5 + 154.2 = 277.98 pounds. So the weight that represents the 99th percentile is approximately 278 pounds.
To find the weight that represents the 36th percentile, we follow the same steps as above. The z-score associated with the 36th percentile is approximately -0.361. Substituting this value into the formula for X, we get:
X = z * standard deviation + mean = -0.361 * 51.5 + 154.2 = 138.51 pounds. So the weight that represents the 36th percentile is approximately 139 pounds.
The third quartile represents the 75th percentile. To find the weight that represents the third quartile, we need to find the z-score associated with the 75th percentile. The z-score can be calculated using the formula mentioned above. For the 75th percentile, the z-score is approximately 0.674. Substituting this value into the formula for X, we get:
X = z * standard deviation + mean = 0.674 * 51.5 + 154.2 = 188.07 pounds. So the weight that represents the third quartile is approximately 188 pounds.