Given probability distributions for time between arrivals and service time

time$\_$between$\_$arrivals $=[0,1,2,3,4,5]$

arrival$\_$probabilities $=[0\mathrm{.}1,0\mathrm{.}35,0\mathrm{.}25,0\mathrm{.}15,0\mathrm{.}1,0\mathrm{.}05]$

service$\_$time $=[1,2,3,4]$

service$\_$probabilities $=[0\mathrm{.}25,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}15]$

# Simulate arrival times for $25$ customers

arrival$\_$times $=$ np$.$random.choice$($time$\_$between$\_$arrivals, size$=25,$ p$=$arrival$\_$probabilities$)$

# Simulate service times for $25$ customers

service$\_$times $=$ np$.$random.choice$($service$\_$time, size$=25,$ p$=$service$\_$probabilities$)$

print$("$Arrival Times:", arrival$\_$times$)$

print$("$Service Times:", service$\_$times$)$

Explanation:

simulate the arrival times of $25$ customers based on the provided probability distribution for time between arrivals.

Similarly, simulate the service times for each customer based on the provided probability distribution for service time.

Step $2$

Step $2$: Calculate Customer Waiting Time and Determine if Criterion is Met

# Assume the bank opens at $8$:$30$ AM

opening$\_$time $=8*60+30$ # Convert opening time to minutes

# Calculate customer start service times

start$\_$service$\_$times $=$ np$.$cumsum$($arrival$\_$times$)+$ opening$\_$time

# Calculate customer end service times

end$\_$service$\_$times $=$ start$\_$service$\_$times $+$ service$\_$times

# Calculate customer waiting times

waiting$\_$times $=$ start$\_$service$\_$times $-$ np$.$roll$($end$\_$service$\_$times, $1)$

waiting$\_$times$[0]=0$ # Set the waiting time of the first customer to $0$

# Check if the average customer waiting time does not exceed $3$ minutes

average$\_$waiting$\_$time $=$ np$.$mean$($waiting$\_$times$)$

if average$\_$waiting$\_$time $<=3$:

print$("$The drive$-$in window meets the criterion. Average customer waiting time:", round$($average$\_$waiting$\_$time, $2),$ "minutes."$)$

else:

print$("$The drive$-$in window does not meet the criterion. Average customer waiting time:", round$($average$\_$waiting$\_$time, $2),$ "minutes."$)$

Explanation:

Calculate the waiting time for each customer as the difference between their arrival time and the time they start receiving service.

Then, check if the average customer waiting time does not exceed $3$ minutes, which is the criterion set by the bank manager.