Question

The mean weight of a class of sixth graders is 103 pounds with a standard deviation of 6.3 pounds. If a student's weight is in the lowest 2.5% of the class, what would be his or her approximate weight?

a) 115.6 pounds
b) 108.4 pounds
c) 96.7 pounds
d) 90.4 pounds

Answer 1

Using the normal distribution and Z-scores for a class with a mean weight of 103 pounds and a standard deviation of 6.3 pounds, a student in the lowest 2.5% weighs approximately 90.4 pounds.

Step-by-step explanation:

If a student's weight is in the lowest 2.5% of the class, we need to use the normal distribution and Z-scores to find this value. Given that the mean weight is 103 pounds and the standard deviation is 6.3 pounds, we look for the Z-score that corresponds to the percentile of 2.5%. This Z-score is approximately -1.96 because it falls 1.96 standard deviations below the mean on a normal distribution.

We can then use the Z-score formula:

1. Z = (X - mean) / standard deviation
2. -1.96 = (X - 103) / 6.3
3. X = -1.96 * 6.3 + 103
4. X ≈ 90.4 pounds

Thus, a student who weighs in the lowest 2.5% of the class would weigh approximately 90.4 pounds, which corresponds to option d).