A distribution has a mean of 70 and a standard deviation of 8. What is the z-score for a value of 82?

The z-score is the number of standard deviations a value lies from the mean: $z=\frac{x-\mu}{\sigma}=\frac{82-70}{8}=\frac{12}{8}=1.5$, choice G. Choice J ($12$) is only the raw difference from the mean and never divides by the standard deviation. Choice F ($1.0$) would result from a standard deviation of $12$ or a value of $78$. Choice H ($1.75$) would require a value of $84$. Because $82$ is $12$ above the mean, and $12$ is one and a half times the standard deviation of $8$, the answer must be $1.5$.