A student observes the elevator usage of a building with a

Reference no: EM13607545

A student observes the elevator usage of a building with a single elevator. This elevator will only allow people to go from the main floor to the 10th of the building. Once passengers are placed on the 10th floor, the elevator will then return back to the main floor, regardless of whether there are people waiting on the main floor or not. The entire trip from the main floor, up to the 10th floor, and back down takes exactly 5 minutes. If there are no people waiting, the elevator will idle on the main floor. If at least 1 person is present, the elevator will take those waiting up to the 10th floor. However, the elevator can only take at most 6 people. If the requested number of users ever exceeds 6, the first 6 people to arrive will be allowed on and the remaining must take the stairs (they do not wait for the elevator to return).

The student notices that people arrive according to a Poisson process with rate ? = 1 per minute.

a) If the elevator just left with 3 people, what is the probability that it will have to leave immediately again after returning from the 10th floor?

b) What is the probability that an elevator must take exactly 4 people?

c) If an elevator has been idle for 30 seconds, what is the expected time until it must make

another trip?

d) A new system is set up where the elevator will only leave immediately if there are 2 or more

people waiting. If there is only a single person, the elevator will wait 1 extra minute before leaving. Given that a passenger waits while an elevator is idle, what is the probability that the extra length of their wait is less than 30 seconds?

e) Assume that the managers decide that instead of waiting for 2 passengers, they prefer 3 passengers to be present before an elevator leaves. However, they also want to ensure that if an elevator must wait, only 50% of the times will it leave before reaching the required 3 people. How long must they set their waiting time for this to happen?

Reference no: EM13607545

Questions Cloud

Houses with and without air conditioners on nine different : houses with and without air conditioners on nine different streets in a certain city are shown below. test at the 5

Air enters a compressor at 100 kpa and 300 k and is : 1. the adiabatic compressor of a large gas turbine receives air from the ambient surroundings at 95 kpa and 20degc

Win co produces a single product its normal selling price : win co. produces a single product. its normal selling price is 26.00 per unit. the variable costs are 16.00 per unit.

When leaping at an angle of 580degree above the horizontal : the froghopper philaenus spumarius holds the world record for insect jumps. when leaping at an angle of 58.0degree

A student observes the elevator usage of a building with a : a student observes the elevator usage of a building with a single elevator. this elevator will only allow people to go

Calculate the bulk density of a rock which has 20 porosity : calculate the bulk density of a rock which has 20 porosity. the bulk mineralogy of the rock is 80 quartz 15 calcite and

What must the bandwidth be for a radar system which uses : what must the bandwidth be for a radar system which uses pulse widths of .1 us? if this radar is used for determining

Jones co can futher process product b to produce product c : jones co. can futher process product b to produce product c. product b is currently elling for 31.00 per pound and

Chuck a dentist raises prize rabbits for breeding and : chuck a dentist raises prize rabbits for breeding and showing purposes. assume that the activity is determined to be a

User Account

All Pages