There are three horses in a race. Historical records show that the time it takes each...

There are three horses in a race. Historical records show that the time it takes each horse to complete a similar race is Normally distributed with a mean and standard distribution given in

the table below (all numbers are in minutes). Simulate 1,000 races using Excel. Approximately what proportion of the time will each horse win?

Horse	Mean	Standard Dev.
1	0.87	0.17
2	0.95	0.06
3	1.10	0.14

Make sure you explain in your write up what each column of your spreadsheet stands for and how you obtained each column from the other data.

Expert Solution

Spreadsheet model for simulation is following

Formula:

B9 =NORMINV(RAND(),B$3,B$4) copy to B9:D1008

E9 =MATCH(MIN(B9:D9),B9:D9,0) copy to E9:E1008

H8 =COUNTIF($E$9:$E$1008,1)/1000 copy to H10, H12

Simulation results:

Proportion of time Horse 1 wins = 0.683

Proportion of time Horse 2 wins = 0.262

Proportion of time Horse 3 wins = 0.055

(note that the above results will vary for every simulation run)

keosha answered 6 months ago

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