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

Question

The driving distance for professional golfer, Lion Woods, varies uniformly between 251 and 276 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 253 and 256 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) 49% 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)plus/minus three standard deviation of the meanplus/minus one standard deviation of the meanNone of theseplus/minus two standard deviation of the mean

Explanation / Answer

Given uniform distribution U(251, 276)
a = 251 and b = 276

As there are 276 - 251 = 25 units between a and b, probability at each unit = 1/25

(A)
Probability that one of his randomly selected drives is between 253 and 256 yards = (256-253)*1/25 = 0.12

(B)
x * 1/25 = 0.37
x = 9.25

This x represents the range of drives.
251 + 9.25 = 260.25

260.25 yards is the 7th percentile of the distribution of his driving distances.

(C)
Var = (1/12)(b-a)^2 = 1/12*(276-251)^2 = 52.08

std. dev. = 7.22

(D)
x * 1/25 = 0.49
x = 12.25

specific distance = 276 - 12.25 = 263.75 yards

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