Larry Ellison starts a company that manufacturers high$-$end custom leather bags. He hires three employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is $1\mathrm{.}7$ days with a standard deviation of $2\mathrm{.}7$ days. Larry expects to receive one customer order per day on average. The inter$-$arrival times of orders have a coefficient of variation of $1.$

What is the expected duration, in days, between when an order is received and when production begins on the bag $($i$.$e$.$ include the time waiting to start production but do not include the time in production$)?($The accuracy should be of two digits after the decimal places.$)$