Queuing analysis is needed in this problem so that various operating characteristics can be understood by management. They may want to know things such as the probability of their server being idle, or how many people are waiting to be served, or how many people are in the entire system $($waiting to be served, as well as being served. All kinds of businesses worry about their customers needing to stand in long lines, such as entertainment parks, like Disney, or restaurants, or medical clinics, or retail check$-$out lines. Sometimes the line involves trucks waiting at a dock, or ships waiting to pull into a port. If the folks in line are too long, the business may choose to add additional servers, or implement technology changes to speed up the process. Sometimes a business may choose to brag about their 'short waits', or no waiting, such as in their advertising to draw customers from their competitors. Even hospitals compete with each other, by posting their Emergency Room wait times, etc...

Supplement F P$1($not available from the textbook$)-$ so use this information and questions:

Trucks using a single$-$server loading dock have a mean arrival rate of $14$ per day. The loading$/$unloading rate is $19$ per day.

What is the probability that the truck dock will be idle?

What is the average number of trucks waiting for service?

What is the average time a truck waits for the loading or unloading service?

What is the probability that a new arrival will have to wait?

What is the probability that more than three trucks are waiting for service?

Please answer ASAP! Thank you!