Assume $x$ is normally distributed with a mean of $10$ and a standard deviation of $2$. What is the z-score for $x=14$?

• A. $1$
• B. $4$
• C. $2$
• D. $0.5$

Answer: (C)

Verified step by step guidance

1. Identify the given information: the random variable \(x\) is normally distributed with mean \(\mu = 10\) and standard deviation \(\sigma = 2\), and we want to find the z-score for \(x = 14\).
2. Recall the formula for the z-score, which standardizes a value from a normal distribution: \[z = \frac{x - \mu}{\sigma}\]
3. Substitute the given values into the formula: \[z = \frac{14 - 10}{2}\]
4. Simplify the numerator by subtracting the mean from the value: \[z = \frac{4}{2}\]
5. Divide the numerator by the standard deviation to find the z-score: \[z = 2\]