Final answer:
The student's question involves calculating and interpreting z-scores for child weights to assess growth according to WHO standards. Z-scores indicate how far and in what direction a data point is from the mean, providing insight into a child's development.
Step-by-step explanation:
The question deals with the calculation of z-scores for given weights to assess child development and growth standards. The z-score is a statistical measurement that describes the number of standard deviations a data point is from the mean of a data set. In this case, it's applied to the measurement of weights for girls who are 80 cm in height.
To calculate the z-scores, we use the formula z = (X - μ) / σ, where X is the weight of the child, μ (mu) is the mean weight, and σ (sigma) is the standard deviation. Based on the given mean (μ = 10.2 kg) and standard deviation (σ = 0.8 kg), the following z-scores are calculated for each weight:
- For 11 kg: z = (11 - 10.2) / 0.8 = 1
- For 7.9 kg: z = (7.9 - 10.2) / 0.8 = -2.875
- For 12.2 kg: z = (12.2 - 10.2) / 0.8 = 2.5
Interpreting these z-scores provides insight into how a child's weight compares to the standard growth pattern for their height and gender. A z-score of 1 means the child's weight is one standard deviation above the mean, z-score of -2.875 indicates the child's weight is almost three standard deviations below the mean, and a z-score of 2.5 signifies the child's weight is two and a half standard deviations above the mean.