Question

1. A robbery has just been committed at the Corner Market in the downtown area of the city. The market owner was able to activate the alarm, and the robber fled on foot. Police officers arrived a few minutes later and asked the owner, “How long ago did the robber leave?” “He left about 10 minutes ago and headed east.”, the owner responded. “He’s probably ten blocks away by now.”, one of the officers said to the other. “Not likely”, said the storeowner. “He was so stoned on drugs that I bet he’s still only within a few blocks of here! He’s probably just running in circles!”
   
   Perform a simulation experiment that will test the storeowner’s hypothesis. Assume the following:
   
   
2. It takes him 1 minute to walk each block (they are short).
3. At the end of each minute interval he is at a corner. There is a 40% chance that he will fall asleep for 1 minute, and a 15% chance that he walk east, or north, or west, or south.

   My suggestion is to run at least 1000 trials of the ten-minute journey of the robber.

4. On average how many block has he walked?
5. On average how far away is he (using blocks - not “diagonals”) from the store?
6. What is the probability he is two blocks or less (walking on streets) from the store?
7. What is a 95% confidence interval estimate of this probability?
   
   This should be done in Excel, please include the Trial too

Answer 1

ANSWER:

Simulation model is as follows

Formula: C11 =RAND()

D11 =LOOKUP($C11,$D$3:$D$7,$A$3:$A$7)

E20 =COUNTIF(D11:D20,"<>"&"Fall asleep")

F20 =ABS(COUNTIF(D11:D20,"Walk North")-COUNTIF(D11:D20,"Walk South"))+ABS(COUNTIF(D11:D20,"Walk East")-COUNTIF(D11:D20,"Walk West"))

Select range A11:F20. Copy and paste this upto row 10010

This will compete the 1000 trials.

I12 =COUNTIF(F11:F10010,"<=2")/1000

I13 =AVERAGE(E11:E10010)

I14 =AVERAGE(F11:F10010)

Probability that he is two blocks or less from the store = 0.433

On average how many blocks he has walked = 7 blocks

On average how far away is he from the store = 3 blocks away

Note that above simulation results will vary with every simulation run. So these will not match from simulation to simulation.