Final answer:
To find the weight corresponding to a z-score of -0.75 with a mean of 10.2 kg and a standard deviation of 0.8 kg, we use the formula X = zσ + μ and calculate X = -0.75 * 0.8 kg + 10.2 kg which equals 9.6 kg.
Step-by-step explanation:
To determine what weight would give a newborn a z-score of -0.75, we need to use the information provided about the reference population of 80 cm girls with a mean weight of 10.2 kg and a standard deviation of 0.8 kg. The z-score represents the number of standard deviations a value is from the mean.
Using the formula for a z-score:
z = (X - μ) / σ
where:
We can rearrange the formula to solve for X:
X = z σ + μ
Substituting in our values:
X = -0.75 × 0.8 kg + 10.2 kg
After calculating, we find:
X = -0.6 kg + 10.2 kg = 9.6 kg
Therefore, a newborn with a z-score of -0.75 would weigh 9.6 kg.