The average transit time for a 16-wheeler from Knoxville to Dallas, Texas (a dis

Question

The average transit time for a 16-wheeler from Knoxville to Dallas, Texas (a distance of about 764 miles) for a certain trucking firm is about 15 hours with a standard deviation of about 3 hours. The distribution of transit time has tended to be skewed left over the past year. (a) If a random sample of 50 transit times is taken, what is the probability that the average transit time would be more than 14 hours? (a) Find the 99th and 1st percentile of average transit times. What value would these numbers have to the trucking firm?

Explanation / Answer

a)
n = 50 , mean = 15 , s = 3
p(x > 14)

z = (x - mean)/( s/sqrt(n))
= ( 14 - 15) /( 3/sqrt(50))
= -2.357
we need to find p(z > -2.357)
P(x > 14) = P( z > -2.357) = 0.9908

b)

z value for 99 percentile = 2.33

By central limit theorem,
z = (x - mean)/( s/sqrt(n))
2.33 = (x - 15) /( 3/sqrt(50))
x = 15.9885

z value for 1st percentile = -2.33

By central limit theorem,
z = (x - mean)/( s/sqrt(n))
-2.33 = (x - 15) /( 3/sqrt(50))
x = 14.0115

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