E$-$mails arrive from $8$ a$.$m$.$ to $6$ p$.$m$.$ at a rate of $10$ e$-$mails per hour $($coefficient of variation for the arrivals is $1).$ At each moment in time, there is exactly one lawyer $"$on$-$call", that is$,$ sitting at his or her desk waiting for incoming e$-$mails. It takes the lawyer, on average, $5$ minutes to write the response e$-$mail. The standard deviation of this is $4$ minutes.

a$)$ What is the average time a customer has to wait for the response to his$/$her e$-$mail? Note: This includes the time it takes the lawyer to start writing the e$-$mail and the actual writing time, i$.$e$.,$ waiting time in queue plus the writing time

b$)$ How many e$-$mails will a lawyer have received at the end a $10-$hour day?

c$)$ When not responding to e$-$mails, the lawyer on call is encouraged to actively pursue cases that potentially could lead to large settlements. How much time in a $10-$hour day can a

My$-$law.com lawyer dedicate to this activity? $($assume the lawyer can instantly switch between e$-$mails and work on a settlement$)?$