Question

The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.4 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 3.6 is P(x = 3.6) =

d. The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.4 mm is P(1.1 < x < 1.5) =

e. The probability that the jump's round off error is greater than 1.98 is P(x > 1.98) =

f. P(x > 5.2 | x > 1.8) =

g. Find the 47th percentile.

h. Find the minimum for the upper quartile.

Answer 1

X ~ U (0 , 5.4)

a) mean = ( 0 + 5.4) / 2 = 2.7

b) standard deviation = (5.4 - 0) / sqrt(12) = 1.56

c) P(X = 3.6) = 0

d) P(1.1 < X < 1.5) = (1.5 - 1.1) / (5.4 - 0) = 0.074

e) P(X > 1.98) = (5.4 - 1.98) / (5.4 - 0) = 0.633

f) P(X > 5.2 | X > 1.8) = P(X > 1.8 and X > 5.2) / P(X > 1.8)

                                   = P(X > 5.2) / P(X > 1.8)

                                   = [(5.4 - 5.2) / (5.4 - 0)] / [(5.4 - 1.8) / (5.4 - 0)]

                                   = 0.2 / 3.6

                                   = 0.056

g) P(X < x) = 0.47

or, (x - 0) / (5.4 - 0) = 0.47

or, x = 2.538

h) P(X < x) = 0.75

or, (x - 0) / (5.4 - 0) = 0.75

or, x = 4.05