a$)$ Over $43,000$ students graduate from NZ universities each year. Graduates work for $40$ years on average until retirement.



How many graduates will be employed in $2050?$ Explain the assumptions that are used in your solution.



b$)$ You are waiting in a line of $15$ customers at a Starbucks and observe that there is only one server, who serves $1$ customer per minute.



$-$ How long would it take to get your coffee?

$-$ You go to Starbucks the next day and observe that one server is added. The two servers $($working together$)$ can now serve $2$ customers per minute. How long it would take to get your coffee if you are in a line of $20$ customers?



c$)$ The New Zealand Heart Foundation plans to install a free blood pressure testing booth in Aotea Centre. Previous experience indicates that, on average, people arrive every six minutes with a standard deviation of two minutes. Blood pressure measurements take five minutes on average with a standard deviation of four minutes as the variety of people arriving requires different procedures.



The Heart Foundation management wishes to examine several queue$-$operating characteristics.



$-$ What is the average number of persons that can be expected to be in line?

$-$ What is the average amount of time that a person can expect to spend in line?

$-$ On average, how much time will it take to measure a person's blood pressure, including waiting time?

$-$ On the weekends, the arrival rate can be expected to decrease to nearly $7\mathrm{.}5$ persons per hour. What effect will this have on the average waiting time?