A concrete delivery truck shuttles between a concrete mixing plant and a constru

Question

A concrete delivery truck shuttles between a concrete mixing plant and a construction site for the entire 10-hr working day. The one-way trip takes on the average 1 hr with a standard deviation of 0.2 hr. Assuming that the travel time can be modeled by a normal distribution:

(A) What is the probability of completeling a two-way (complete) trip within 1.5 hr?
(B) Within 2.5 hr?

(C) Assuming that the time needed to unload the truck is also a normal variate with a mean of 0.5 hr and standard deviation of 0.2 hr, what are the mean and standard deviation of the time required for a complete two-way trip with unloading?

Explanation / Answer

A) new std= v[(0.2)2 * (0.2)2] = 0.28 So Prob. of <1.5hrs, using mean=2, std=0.28 is = 0.037
B) So Prob. of <2.5hrs, using mean=2, std=0.28 is = 0.96
C) New std= v[(0.2)2 * (0.2)2 * (0.2)2 ]= 0.35 So, mean=1+1+0.5=2.5, std=0.35
So, mean=1+1+0.5=2.5, std=0.35

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