Question

There are two ways for a concrete truck to go from a ready-mixed concrete plant to the construction site. The first way is direct, for which the mean and standard deviation of travel time are 30 min and 5 min, respectively. The second way is through Town A. The mean and standard deviation of travel time between the plant and Town A are 14 min and 5 min, respectively. The mean and standard deviation of travel time between Town A and the construction site are 14 min and 6 min, respectively. If the total travel time is above 45 min, the concrete in the truck will go bad. Calculate the probability that the concrete goes bad for both cases of choosing the direct and indirect ways. Assume travel time has a normal distribution.

Answer 1

DIRECT WAY TO  go from a ready-mixed concrete plant to the construction site..

MEAN= 30 MIN

SD= 5MIN

P(X>45min)

P ( X>45 )=P ( X−μ>45−30 )=P ((X−μ)/σ>(45−30)/5)

Since Z=(x−μ)/σ and (45−30)/5=3 we have:

P ( X>45 )=P ( Z>3 )

Use the standard normal table to conclude that:

P (Z>3)=0.0013

The second way is through Town A:

MEAN=14 MIN

SD= 6min

P ( X>45 )=P ( X−μ>45−14 )=P ((X−μ)/σ>(45−14)/6)

Since Z=(x−μ)/σ and (45−14)/6=5.17 we have:

P ( X>45 )=P ( Z>5.17 )

Use the standard normal table to conclude that:

P (Z>5.17)=0.000