The driving distance for professional golfer, Lion Woods, varies uniformly betwe

Question

The driving distance for professional golfer, Lion Woods, varies uniformly between 246 and 271 yards.

(Round probabilities to four decimals and yardage to two decimals)

a) What's the probability that one of his randomly selected drives is between 248 and 251 yards?

b) What's the 37th percentile of the distribution of his driving distances?

c) What's the standard deviation of his driving variance?

d) 44% of his drives are longer than a specific distance. Find that specific distance.

e) Approximately 68% of his driving distances fall between (Click to select)None of theseplus/minus one standard deviation of the meanplus/minus two standard deviation of the meanplus/minus three standard deviation of the mean

Explanation / Answer

Solution:

here as it is uniformely disributed with parameter a=246 and b=271

hence its cumulative frequency distribution P(X<x)=(x-246)/(271-246)=(x-246)/25

a) probability that one of his randomly selected drives is between 248 and 251 yards = (251-248)/25 = 0.12

b) 37th percentile of the distribution of his driving distances =246+0.37*(271-246) = 255.25

c) standard deviation of his driving variance =(b-a)/(12)^1/2 = 271-246/sqrt(12) = 7.2169

d) 44% of his drives are at (100-44=56 percentile) hence specific distance 246+0.56*(271-246) = 260

e)Approximately 68% of his driving distances fall between plus/minus one standard deviation of the mean

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