The driving distance for the top 100 golfers on the PGA touris between 284.7 and

Question

The driving distance for the top 100 golfers on the PGA touris between 284.7 and 310.6 yards. Assume that the drivingdistance for these golfers is uniformly distributed over thisinterval. a. Give a mathematical expression for the probability densityfunction of driving distance b. What is the probability for driving distance for one ofthese golfers is less than 290 yards. c. What is the probability the driving distance for one ofthese golfers is at least 300 yards. d. What is the probability the driving distance for one ofthese golfers is between 290 and 305 yards. e. How many of these golfers drive the ball at least 290yards. The driving distance for the top 100 golfers on the PGA touris between 284.7 and 310.6 yards. Assume that the drivingdistance for these golfers is uniformly distributed over thisinterval. a. Give a mathematical expression for the probability densityfunction of driving distance b. What is the probability for driving distance for one ofthese golfers is less than 290 yards. c. What is the probability the driving distance for one ofthese golfers is at least 300 yards. d. What is the probability the driving distance for one ofthese golfers is between 290 and 305 yards. e. How many of these golfers drive the ball at least 290yards.

Explanation / Answer

Part a:    f(x)= 1/(25.9), for 284.7 < x < 310.6    f(x)= 0, elsewhere Part b:    P(284.7 < x < 290) = (290-284.7)/25.9= 0.2046 Part c:    P(x>300) = (310.6-300)/25.9 =0.4093 Part d:    P(290 < x < 305) = (305-290)/25.9 =0.5792 Part e:    P(x>290) = (310.6 - 290)/25.9 =0.7954    (100 golfers)*(0.7954) = 79.53 = 79 golfers(since I cannot have partial people)

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