Probability of Studying More Than 8 Hours

A recent study found that the amount of time (in hours) a group of students spent studying for a mathematics exam followed a normal distribution with a mean of 6 hours and a standard deviation of 2 hours. Assuming that the time spent studying is normally distributed, answer the following question.

What is the probability that a randomly chosen student studied for more than 8 hours? To find this probability, calculate the z-score for 8 hours and then use the standard normal distribution.

Use the z-score formula: $$ z = \frac{x - \mu}{\sigma} $$ where $x$ is the value of interest, $\mu$ is the mean, and $\sigma$ is the standard deviation.