Traveling between two campuses of a university in a city via shuttle bus takes, on average, 28 minutes with a standard deviation of 5 minutes. in a given week, a bus transported passengers 40 times. what is the probability that the average transport time was more than 30 minutes? assume the mean time is measured to the nearest minute.
Answers
Given : Traveling between two campuses of a university in a city via shuttle bus takes, on average, 28 minutes with a standard deviation of 5 minutes.
in a given week, a bus transported passengers 40 times.
To Find : what is the probability that the average transport time was more than 30 minutes
Solution:
Mean = 28 mins
SD = 5 mins
Value = more than 30 mins
Z score = ( Value - Mean)/SD
=> Z score = ( 30 - 28)/5 = 2/5
= 0.4
65.54 % below 30 minutes
More than 30 minutes = 100 - 65.54 % = 34.46 %
Probability = 0.3446
Considering whole numbers and approximating
Times = (34.46/100) * 40 = 13.78 ≈ 14
Probability = 14/40 = 0.35
probability that the average transport time was more than 30 minutes = 0.35
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