If Cynthia's test score is $1.5$ standard deviations above the mean, what is her $z$-score in the standard normal distribution?

• A. $-1.5$
• B. $2.0$
• C. $1.5$
• D. $0$

Answer: (C)

Verified step by step guidance

1. Understand that a z-score represents how many standard deviations a data point is from the mean in a standard normal distribution.
2. Identify the information given: Cynthia's test score is 1.5 standard deviations above the mean.
3. Recall the formula for a z-score: \(\text{z-score} = \frac{X - \mu}{\sigma}\), where \(X\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
4. Since Cynthia's score is 1.5 standard deviations above the mean, her z-score is simply +1.5, indicating her score is 1.5 standard deviations above the mean.
5. Therefore, the z-score corresponding to Cynthia's test score is \(+1.5\).