As an airport manager, it is your job to assign gates to specific flights. However, flights rarely arrive exactly at the scheduled time. Sometimes flights land early and sometimes they land late. You are currently trying to determine which gate a flight from Chicago to Reno should be assigned to. The scheduled arrival time for the daily flight is 10:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 10:07 am and a late arrival time of 10:47 am.

a. Calculate the mean and the standard deviation of the distribution in minutes. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b. What is the probability that a flight arrives late (later than 10:25 am)? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimalplaces.)