Suppose the birth weights of newborns in a population are normally distributed with a mean of $3.5$ kg and a standard deviation of $0.5$ kg. What is the z-score of a newborn who weighs $4$ kg?

• A. $\frac{4-3.5}{1}=0.5$
• B. $\frac{4-3.5}{0.5}=1$
• C. $\frac{3.5-4}{0.5}=-1$
• D. $\frac{4-3.5}{0.25}=2$

Answer: (B)

Verified step by step guidance

1. Identify the given information: the mean birth weight \(\mu = 3.5\) kg, the standard deviation \(\sigma = 0.5\) kg, and the specific newborn's weight \(X = 4\) kg.
2. Recall the formula for the z-score, which standardizes a value by measuring how many standard deviations it is from the mean: \(z = \frac{X - \mu}{\sigma}\)
3. Substitute the given values into the formula: \(z = \frac{4 - 3.5}{0.5}\)
4. Simplify the numerator by subtracting the mean from the observed value: \$4 - 3.5 = 0.5$
5. Divide the result by the standard deviation to find the z-score: \(z = \frac{0.5}{0.5}\)