Question

In: Operations Management

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.

Solutions

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 2 weeks ago
Next > < Previous

Related Solutions

10 horses from three different stables participate in a race. 5 horses come from stable A,...
10 horses from three different stables participate in a race. 5 horses come from stable A, 3 from stable B and 2 from stable C. A) Calculate the number of possible results for the ten horses. B) Calculate the number of possible results by grouping the horses by stable. c) For a trifecta(tierced), we choose the horses that will win the three first places in order. Calculate the number of possible trifecta(tierced). d) Calculate the number of possible trifecta(tierced) by...
4. In a race with 8 horses, in how many ways can the race end with...
4. In a race with 8 horses, in how many ways can the race end with the first, second, and third place winners? 5. For one week in May, an insurance agent kept records of the number of prospective clients (x) with whom she had consulted and the number of them who had purchased a policy (y). a. Find the correlation coefficient r b. Find the coefficient of determination ?2 c. What percentage of the variation in the number of...
A horse race contains 8 horses. If you wished to bet on every possible top three...
A horse race contains 8 horses. If you wished to bet on every possible top three finishes (first, second, and third place), how many bets would you need to place? The following represents a binomial experiment. Seven plants are operated by a garment manufacturer in seven different countries. There is a 10% chance of strike at any time. It is also believed that strikes at one plant do not influence strikes at any other plant (because these are in third...
Historical records show that in 1960 the average household size with 3.29 people with a standard...
Historical records show that in 1960 the average household size with 3.29 people with a standard deviation of 1.20 people in 2017 a sample 25 households in Richmond Virginia showed and mean number of residents per house where were 3.91 at a 0.1 significance level is it reasonable to conclude the mean number of residents in Richmond Virginia today is different from the typical American household in 1960? a. in the above problem, the critical values are (round to four...
A race car driver tested his car for the time it takes to go from 0...
A race car driver tested his car for the time it takes to go from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. These times are known to be normally distributed. What is the value of t used to construct a 95% confidence interval for the mean time it takes the car to go from 0 to 60? Round your answer to 2 decimal places.
1.Historical records show that the average per capita consumption of eggs in the US is 278...
1.Historical records show that the average per capita consumption of eggs in the US is 278 (this is per year). Lately, consumers have been getting conflicting advice about the benefits and dangers of eggs, and a rural agricultural association wants to know if the average egg consumption has changed. A sample of 50 adults yielded a sample mean egg consumption of 287 eggs and a sample standard deviation of 28 eggs. Construct a null and alternate hypothesis that the association...
Professor Moore, who lives a many miles outside a college town, records the time he takes to drive to the college each morning.
  Professor Moore, who lives a many miles outside a college town, records the time he takes to drive to the college each morning. Below are the times (in minutes) for 22 consecutive weekdays. The data are contained in the gray columns in the following table and have been ordered from smallest to largest. Observation    Driving Time (min) Observation    Driving Time (min) 1 52 12 62.7 2 57.9 13 63.7 3 58.2 14 64.9 4 59 15 65.8...
university adminststors have historical records that indicate that between august and oct 2013 tge meant time...
university adminststors have historical records that indicate that between august and oct 2013 tge meant time between hits in the UTD himeoage was 2 min they dupect that in fact the mean time between hits has decreased ie traffic is up sampling 50 interarrival times fron records for nicemeberb2013 guces c of 1.7 min and s if 1.9 min
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records...
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to during the current year. In addition, it estimates that of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years (to 1...
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records...
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that  of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to  during the current year. In addition, it estimates that  of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years (to 1 decimal)?    b....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT