$4.$A$\mathrm{.}4$ Mr$.$ Streep takes the bus every workday. In the morning, his waiting times are uniformly distributed on the interval $0,10$ minutes. In the evening, his waiting times are uniformly distributed on the time interval $0,15$ minutes. Assume that all waiting times are independent.

a$.$ Calculate the expectation and the standard deviation of his total waiting time during a $5-$day workweek.

b$.$ Calculate the expected difference between his total waiting time in the evening and his total waiting time in the morning during a $5-$day workweek.