In a study of students' test scores, researchers found that the mean score for a sample of 100 students was 78 with a standard deviation of 10. Assuming that the scores are normally distributed, what is the probability that a randomly selected student scored less than 85?
Use the Z-score formula: $$Z = \f\frac{X - \mu}{\sigma}$$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation.