Sure, let's solve this step by step.
First, recall what a z-score represents. A z-score indicates how many standard deviations an element is from the mean of the population. The formula to convert a z-score to the corresponding weight is:
[tex]\[ \text{weight} = \text{mean} + (\text{z-score} \times \text{standard deviation}) \][/tex]
We are given the following values:
- The mean weight of the population (\(\mu\)) is 22 grams.
- The standard deviation (\(\sigma\)) of the population is 13 grams.
- The z-score (\(z\)) is -0.75.
Now plug these values into the formula:
1. Multiply the z-score by the standard deviation:
[tex]\[ -0.75 \times 13 = -9.75 \][/tex]
2. Add this result to the population mean:
[tex]\[ 22 + (-9.75) = 22 - 9.75 = 12.25 \][/tex]
So, the weight that would give a newborn a z-score of -0.75 is 12.25 grams.
