Question

The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 4.6 mm. Round values to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the round off error for a jumper's distance is exactly 4.3 is P(x = 4.3) = d. The probability that the round off error for the distance that a long jumper has jumped is between 0 and 4.6 mm is P(1.4 < x < 3.7) = e. The probability that the jump's round off error is greater than 3.22 is P(x > 3.22) = f. P(x > 3.7 | x > 0.1) = g. Find the 7th percentile. h. Find the minimum for the lower quartile.

Answer 1

X ~ U (0 , 4.6)

a) mean = (4.6 + 0) / 2 = 2.3

b) standard deviation = (4.6 - 0) / sqrt(12) = 1.3279

c) P(X = 4.3) = 0

d) P(1.4 < X < 3.7) = (3.7 - 1.4) / (4.6 - 0) = 0.5

e) P(X > 3.22) = (4.6 - 3.22) / (4.6 - 0) = 0.3

f) P(X > 3.7 | X > 0.1) = P(X > 3.7 and X > 0.1) / P(X > 0.1) = P(X > 3.7) / P(X > 0.1) = [(4.6 - 3.7) / (4.6 - 0)] / [(4.6 - 0.1) / (4.6 - 0)] = 0.2

g) P(X < x) = 0.07

or, (x - 0) / (4.6 - 0) = 0.07

or, x = 0.322

h) P(X < x) = 0.25

or, (x - 0) / (4.6 - 0) = 0.25

or, x = 1.15