Premanufactured wooden roof trusses allow builders to complete projects faster and with lower on-site labor costs. The connector plates for trusses are made from Grade A steel and are hot-dip galvanized. The thickness of a truss connector (in inches) varies lightly and has a uniform distribution with a = 0.036 and b = 0.050.
a. If the manufacturer will only use connectors with a minimum thickness of 0.04 inch, what proportion of connectors is rejected?
b. Suppose a truss connector is selected at random. Find the probability that the truss connector has a thickness between 0.042 and 0.045 inch.
c. Find the mean, variance, and standard deviation of the thickness of a truss connector.
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?