f) Find the 5th percentile of the distribution of haul times. In a road-paving p
ID: 2921564 • Letter: F
Question
f) Find the 5th percentile of the distribution of haul times.
In a road-paving process, asphalt mix is delivered to the hopper of the paver by trucks that haul the material from the batching plant. The article "Modeling of Simultaneously Continuous and Stochastic Construction Activities for Simulation" U. of Construction Engr. and Mgmnt., 2013: 1037-1045) proposed a normal distribution with mean value 8.46 min and standard deviation .913 min for the rv X = truck haul time a. What is the probability that haul time will be at least 10 min? Will exceed 10 min? b. What is the probability that haul time will exceed 15 min? C. What is the probability that haul time will be between 8 and 10 min? d. What value c is such that 98% of all haul times are in the interval from 8.46-c to 84.6 c? e. If four haul times are independently selected, what is the probability that at least one of them exceeds 10 min?Explanation / Answer
a)probability that haul time will be at least 10 minute or exceed 10 minute =P(X>10)=1-P(X<10)
=1-P(Z<(10-8.46)/0.913)=1-P(Z<1.6867)=1-0.9542=0.0458
b)P(X>15) =1-P(X<15) =1-P(Z<7.1632)=1-~1 =0.0000
c)P(8<X<10)=P(-0.5038<Z<1.6867)=0.9542-0.3072=0.6470
d)for 98% confidence interval ; z=2.326
therefore c=mean +z*std deviaiton=10.584
e)as Probability to exceed 10 =0.0458
therefore probability that at least one of them exceed 10 min=1-P( none of them exceed)=1-(1-0.0458)4
=0.1711
f)for 5h percentile ; z=-1.645
therefore corresponding value =mean +z*std deviaiton=8.46-1.645*0.913 =6.958
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