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WS 26_How does 1 ATM work^
Name# Please show all steps and all work to receive full credit. When doing this think of what we have done for the project. An excerpt of the records of ATM usage at^ People’s Bank^ for two weeks is given below.^ Arrival Times (in minutes)After Start of Hour
Times (in minutes) Until andBetween Arrivals Week 1 Week 2 Week 1^ Week 2 0.02 0.10 0.53 0.38 2.36 0.94 2.50 2.
1.^ Use the given information to compute an estimate of the mean time between arrivals.^ Remember to show work or explain what you did. 2.^ Let^ A^ be the continuous random variable that gives the time (in minutes) until the first arrival or between consecutive arrivals. Use the resultfrom Part 1 and the assumption that^ A^ has an exponential distribution to find a formula for the
c.d.f.^ of^ A.
Use the following to answer questions 5- 11. Write answer in the boxes given –as if you are filling in the cell with the answer^ (If you’re not sure how to calculate this use Queue Focus to help you) Excerpts of the sheets^ Data^ and^ 1 ATM^ in^ Queue Focus.xls^ are given below. Data 1 ATM. 3.^ Use the result from Problem 2 and the value in cell C35 of^ 1 ATM
to compute the missing value in cell F35.
10.^ An excerpt of the results of one simulation of customer arrival times and service times for two ATMs is given below^ Summary of 2,000 Hours^ Number^ Sum of^ Maximum^ That^ Numbers^ Number in^ Arrive^ in Queue^ Queue
Sum of Total^ Maximum^ Numbers^ Total Number^ Present^ Present 230,622 1,452,235 31 2,752,433^61 The bank manager plans to advertise the claim that the mean number in the queue will not exceed five. Based only on the given information,does it appear that this claim can be substantiated with two ATMs?
11.^ Which of the data given will use Bootstrapping method for the simulation?12.^ Which of the data given will use Monte Carlo method for the simulation?
13.^ On the following table is from a survey of students from the U of A. The students were asked how many hours a week do they spend studying. Using functions and thetool “histogram” in Excel, the follow summary and frequency table was created (column 2 and 3) t is a continuous random variable of the number of study hours.One column has relative frequency,^ f ( t ), only partially done (remember these are probabilities and the sum equals 1) T We want to make a^ pdf^ (the area under the curve equals 1.) We must adjust the height,^ f
( t ), T (i) Finish filling in the missing values of the Relative Frequencies( ) f^ t^ (ii) Fill in the table for^ - adjusted height - which is the^ pdf^ ( round your answer to 4 decimal placesT
) (iii) On the graph provided, make the^ pdf^ of the study hours. Include^ titles and values on the vertical and horizontal axes
. Note that time is a continuous random variable-curve not rectangles for this distribution
The^ pdf^ of Study Hours
Study time hours a week, students spend on all their classes SUMMARY^ TABLE^ Total^ min^ mean^ max^ range^
Bin Width 200 0 10.3 (^29 29 6) FREQUENCY TABLE Relative^ ( ) f^ t Bin Bin Frequency Frequency T 0<= t <=6 (^6 25) 6< t <=12 12 108 0.54 12< t <=18 (^18 50) 18< t <=24 24 15 0.075 24< t <=30 30 2 0.01 Total 200 1
