# Simulation

Suppose a golf club company has designed a new club, which it claims will allow a professional golfer to make a hole-in-one 20% of the time and an amateur golfer 10% of the time. Professional and amateur golfers sign up to play 5 games of 18 holes each.Part A: Design and conduct a simulation to estimate the likelihood that the professional golfer will sink at least four holes-in-one during a single game. Be sure to explain the representations and show all the work for your trials and outcomes. (6 points)

Part B: Design and conduct a simulation to estimate the likelihood that the amateur golfer will sink at least four holes-in-one during a single game. Be sure to explain the representations and show all the work for your trials and outcomes. (6 points)

Part C: Design a study to test the new golf club to see if it causes amateur golfers to perform better than with the currently used club. Remember to give enough detail that your study can be replicated. (6 points)

Part D: Suppose a study was conducted using professional golfers and found the following data:

Old Club New Club
Holes-in-One 30 55
Total Swings Tested 200 225

Construct and interpret 90% confidence intervals for the data. What conclusions can you draw? Be sure to show all work. (6 points)

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