Babies born weighting 2500 grams (about 5.5 pounds) or less are called low-birth-weight babies, and this condition sometimes indicates health problems for the infant. The mean birth weight for children born in a certain country is about 3462 grams (about 7.6 grams). The mean birth weight for babies born one month early is 2655 grams. Suppose both standard deviations are 450 grams. Also assume that the distribution of births weights is roughly unimodal and symmetric. What is the standardized score (z-score), relative to all births in the country,for a baby with a birth weight of 2500 grams?
Z = (score-mean)/SD = (2500-3462)/450 = ?
To calculate the standardized score (z-score), we can use the formula:
z = (x - μ) / σ
Where:
- x is the observation (birth weight in this case)
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
In this case, the observation (birth weight) is 2500 grams.
Given:
- The mean birth weight for children born in the country is μ = 3462 grams.
- The standard deviation for the birth weights in the country is σ = 450 grams.
Using the formula, we can calculate the z-score as follows:
z = (2500 - 3462) / 450
z = (-962) / 450
z ≈ -2.138
Therefore, the standardized score (z-score) for a baby weighing 2500 grams, relative to all births in the country, is approximately -2.138.