Final answer:
To calculate z-scores for given weights using the normal distribution, subtract the mean from the weight and then divide by the standard deviation. The z-score represents the number of standard deviations a weight is from the mean. A z-score can be positive or negative, indicating weights above or below the mean respectively.
Step-by-step explanation:
The weights of newborn children in India follow a Normal Distribution with a mean of 3.4 kg and a standard deviation of 0.57 kg. To calculate the z-scores for the given weights as per the World Health Organization measurements, where weights of 80 cm girls are normally distributed with a mean μ = 10.2 kg and standard deviation σ = 0.8 kg, we can use the formula:
Z = (X - μ) / σ
- For a weight of 11 kg, the z-score would be: Z = (11 - 10.2) / 0.8 = 1
- For a weight of 7.9 kg, the z-score would be: Z = (7.9 - 10.2) / 0.8 = -2.875
- For a weight of 12.2 kg, the z-score would be: Z = (12.2 - 10.2) / 0.8 = 2.5
A z-score indicates how many standard deviations an element is from the mean. A positive z-score indicates a weight above the mean, while a negative z-score indicates a weight below the mean.
Newborns' birth weight is an important measure of infant health, as low birth weight can increase the risk of infant mortality and developmental delays. The average birth weight is centered around 3.4 kg for a full-term infant.