Each week you take a train to visit your Aunt Tillie. The total trip time can be
ID: 2625758 • Letter: E
Question
Each week you take a train to visit your Aunt Tillie. The total trip time can be as short as 20 minutes or less, but the train almost always arrives late and experiences delays as well, so it averages 50 minutes. On really bad weeks, it can take 80 minutes or more. The standard deviation of the travel time, you've found, is ten minutes, and being a really observant statistics student, you realize that trip times have a normal distribution.
(a) What percentage of train trips take between 45 and 50 minutes?
(b) What percentage of trips take more than 65 minutes?
(c) What percentage of trips exceed forty minutes?
(d) What percentage of trips take between 60 and 70 minutes?
Explanation / Answer
mean = 50; stdev = 10
Z = (xbar - mean)/(stdev)
a) percentage of train trips take between 45 and 50 minutes
= P[Z = (50 - 50)/10] - P[Z = (45 - 50)/10]
= P[Z = 0] - P[Z = -0.5]
= 0.5 - 0.3085
= 0.1915 = 19.15%
b) percentage of trips take more than 65 minutes
= 1 - P[Z = (65 - 50)/10]
= 1 - P[Z = 1.5]
= 1 - 0.9332
= 0.0668 = 6.68%
c) percentage of trips exceed forty minutes
= 1 - P[Z = (40 - 50)/10]
= 1 - P[Z = -1]
= 1 - 0.1587
= 0.8413 = 84.13%
d) percentage of trips take between 60 and 70 minutes
= P[Z = (70 - 50)/10] - P[Z = (60 - 50)/10]
= P[Z = 2] - P[Z = 1]
= 0.9772 - 0.8413
= 0.1359
= 13.59%
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