Final answer:
Being in the 10th percentile means Nikoleta is shorter and lighter than 90% of peers in her age group, a potential concern if she was previously at the 50th percentile. Z-scores help interpret how weights compare to the mean of a normally distributed reference population. Understanding percentiles and probabilities is important in assessing growth patterns.
Step-by-step explanation:
If Nikoleta is in the 10th percentile for length and weight, it means that she is shorter and lighter than 90% of children in her reference group. Being in the 50th percentile at birth, which represents the median, is typically considered desirable, as it indicates that she was right in the middle range of her peers. However, dropping to the 10th percentile could be a sign of concern, especially if the decline in her growth percentile was rapid or significant. It is important to monitor her development to ensure she does not have any underlying health issues or nutritional deficiencies that need to be addressed.
According to the World Health Organization, the weights for all 80 cm girls in the reference population are normally distributed with a mean (μ) of 10.2 kg and a standard deviation (σ) of 0.8 kg. To calculate the z-scores for the given weights, we can use the formula: z = (X - μ) / σ. Here's how we calculate the z-scores for the provided weights:
- For 11 kg: z = (11 - 10.2) / 0.8 = 1. This means the weight is 1 standard deviation above the mean.
- For 7.9 kg: z = (7.9 - 10.2) / 0.8 = -2.875. This indicates the weight is approximately 2.875 standard deviations below the mean.
- For 12.2 kg: z = (12.2 - 10.2) / 0.8 = 2.5. This weight is 2.5 standard deviations above the mean.
The median is the value in the middle of a data set and the 15th and 85th percentiles represent the values below which 15% and 85% of the data fall, respectively. The theoretical probability that a randomly chosen pinkie length is more than 6.5 cm corresponds to the proportion of data above this value. If 6.5 cm is at the 85th percentile, there is a 15% probability that a randomly chosen pinkie length is more than 6.5 cm.