Suppose a population has a mean of $\mu =50$ and a standard deviation of $\sigma =8$. What is the z-score for a value of $x=66$? Round your answer to two decimal places as needed.

• A. $2.00$
• B. $2.25$
• C. $1.75$
• D. $1.50$

Answer: (A)

Verified step by step guidance

1. Identify the given values: the population mean \( \mu = 50 \), the population standard deviation \( \sigma = 8 \), and the value for which you want to find the z-score \( X = 66 \).
2. Recall the formula for the z-score, which measures how many standard deviations a value is from the mean: \[ Z = \frac{X - \mu}{\sigma} \]
3. Substitute the given values into the formula: \[ Z = \frac{66 - 50}{8} \]
4. Calculate the numerator (the difference between the value and the mean) and then divide by the standard deviation to find the z-score.
5. Interpret the z-score as the number of standard deviations the value 66 is above the mean of 50.