At the local post office, customers join a single line where they are routed to the first available of $4$ postal service workers for help with their transaction, e$.$g$.$ purchasing postage, weighing the package, answering questions. The time it takes the postal service worker to complete the transaction is $5\mathrm{.}4$ minutes on average with a standard deviation of $3\mathrm{.}3$ minutes. During the busy holiday rush, customers arrive at the post office every $2$ minutes on average with a standard deviation of $1\mathrm{.}4$ minutes.

Calculate the average time in minutes a customer spends waiting in line before service.

Carry intermediate calculations to at least $3$ decimal places.

Enter your final answer rounded to one decimal place.