The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

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Find the \(z\)-score:

$$ z=\frac{x-\mu}{\simga} $$ $$ z=\frac{35-30}{5} $$ $$ z= 1 $$

We can use the empirical rule here; one standard deviation away from the mean correspond to a 68% probability. The tails will be 16% each.

We can also use the \(z\)-table. A \(z\)-score of 1 corresponds to the 84th percentile. 16% will be above this value and correspond to the area where the student is late.