The time a group of high school students arrive home from school each day was found to be normally distributed

Question

the mean time was 3:15 PM and the times had a standard deviation of 15 min. what is the probability that a studnet chosen at random arrives home from school before 2:30 PM?

Answer 1

2:30 is 45 minutes before the mean. This is three standard deviations. You can look up the probability that something is greater than -3 s.d. in a table. You will find that the probability is 0.9987 that they arrive after 2:30 -- making the probability of getting home before 2:30 = 0.0013