Solve these problems and upload your solution to Canvas. You can solve them $$by hand$$ or

using Excel.

Show all your work $($typed in the document or pasting a scanned image of your handwritten

solution$).$ Save your solution document in a $.$pdf file and upload it to Canvas along with an

Excel file for calculations performed in Excel.

Problem $1(12$ points$)$

Many of a bank$$s customers use its automatic teller machine to transact business after normal

banking hours. During the early evening hours in the summer months, customers arrive at a certain

location at the rate of one every other minute. This can be modeled using a Poisson distribution.

Each customer spends an average of $100$ seconds completing his or her transactions. Transaction

time is exponentially distributed.

a$.$ Determine the average time customers spend at the machine, including waiting in line and

completing transactions.

Note: Do not round intermediate calculations. Round your answer to the nearest whole

number.

b$.$ Determine the probability that a customer will not have to wait upon arriving at the automatic

teller machine.

Note: Round your answer to $2$ decimal places.

c$.$ Determine the average number of customers waiting to use the machine.

Note: Round your answer to $2$ decimal places.

Student name: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$Ch $18$ Procedure Problems EM$3310$

Problem $2(12$ points$)$

Trucks are required to pass through a weighing station so they can be checked for

weight violations. Trucks arrive at the station at the rate of $40$ an hour between $7$:$00$

p$.$m$.$ and $9$:$00$ p$.$m$.$ Currently two inspectors are on duty during those hours, each of

whom can inspect $25$ trucks an hour.

a$.$ How many trucks would you expect to see at the weighing station, including those

being inspected?

Note: Round your answer to $3$ decimal places.

b$.$ If a truck was just arriving at the station, about how many minutes could the driver

expect to be at the station?

Note: Round your answer to $2$ decimal places.

c$.$ What is the probability that both inspectors would be busy at the same time?

Note: Round your answer to $4$ decimal places.

Student name: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$Ch $18$ Procedure Problems EM$3310$

Problem $2(12$ points$)$

Trucks are required to pass through a weighing station so they can be checked for

weight violations. Trucks arrive at the station at the rate of $40$ an hour between $7$:$00$

p$.$m$.$ and $9$:$00$ p$.$m$.$ Currently two inspectors are on duty during those hours, each of

whom can inspect $25$ trucks an hour.

a$.$ How many trucks would you expect to see at the weighing station, including those

being inspected?

Note: Round your answer to $3$ decimal places.

b$.$ If a truck was just arriving at the station, about how many minutes could the driver

expect to be at the station?

Note: Round your answer to $2$ decimal places.

c$.$ What is the probability that both inspectors would be busy at the same time?