Let denote the amount of time, to the nearest whole minute, that a city bus takes to go from one end of its route to the other. Assume that has the following probability distribution.

Amount of time (nearest minutes)	47	48	49	50	51	52
Probability (=)	0.10	0.21	0.30	0.25	0.09	0.05

with negligible probability for other values of .

a) What is the probability that the bus takes at most 50 minutes to complete its route?

b) Find the expected (or mean) time the bus takes to complete its route.

c) Find the standard deviation of the amount of time the bus takes to complete its route. Round your answers to 4 decimal places.