SOLUTION: Determine x such that the probability that you will wait less than x minutes is 0.47? The time between arrivals of taxis at a busy intersection is exponentially distributed with a

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Question 1131616: Determine x such that the probability that you will wait less than x minutes is 0.47? 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) About Me  (Show Source):
You can put this solution on YOUR website!
The probability function for an exponential distribution is given by:
P%28x%29+=+lambda%2Ae%5E%28-lambda%2Ax%29
An exponential distribution has a mean of 1%2Flambda
Therefore, lambda+=+1%2F26.23+=+0.03812
To find the probability of waiting less than X minutes, we have to integrate P(x) from 0 to x<=X

Evaluating the integral from 0 to X and taking the log of both sides, we get:
ln%280.53%29+=+-lambda%2AX+-%3E+X+=+16.6547
Ans: 16.6547 mins