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

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) (Show Source): You can put this solution on YOUR website!
The probability function for an exponential distribution is given by:

An exponential distribution has a mean of
Therefore,
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:

Ans: 16.6547 mins
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