Question 1131697: Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 9 minutes? The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 26.23 minutes.
(Please enter your answers as fractions in lowest terms or as decimals rounded to four decimal places. Thank you!)
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The exponential probability distribution can be written as:
P(x) = k*exp(-kx), where k is a constant
The mean of this distribution is given by 1/k
Since the taxi arrivals are independent random events, the fact that you have
already been waiting an hour has no bearing on what happens in the next 9
minutes.
To determine P(60 <= x <= 69), we need to integrate P(x) from 60 to 69,
with k = 1/26.23 = 0.03812
The indefinite integral is -exp(-kx)
Thus P(60 <= x <= 69) = -(exp(-0.03812*69) - exp(-0.03812*60)) = 0.02949
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