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Travel and Transportation

When the Department of Transportation (DOT) repaints the center lines, edge lines, or no-passing-zone lines on a highway, epoxy paint is sometimes applied. This paint is more expensive than latex but lasts longer. If this paint splashes onto a vehicle, it has to be completely sanded off, and that area of the vehicle has to be repainted. The DOT has warned motorists that the drying time for this epoxy paint (in minutes) has a uniform distribution with a = 30 and b = 60. Suppose epoxy paint is applied to a small section of center line.

a. What is the probability that the paint will be dry within 45 minutes?

b. What is the probability that the paint will be dry in between 40 and 50 minutes?

c. Find a value t such that the probability of the paint taking at least t minutes to dry is 0.75.

d. If the DOT road crew removes all of the cones on the center line 55 minutes after painting, what is the probability that the paint will still be wet?

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