SOLUTION: The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 26.23 minutes. Determine x such that the probability that you will wait more t

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Question 1131591: The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 26.23 minutes. Determine x such that the probability that you will wait more than x minutes is 0.23? Determine x such that the probability that you will wait less than x minutes is 0.47?

(Please enter your answers as fractions in lowest terms or as decimals rounded to four decimal places. Thank you!)

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
the mean is 1/26.23=0.0381
wait more than x minutes is e^(-0381x)=0.23
take ln both sides so that -0.0381x=ln(0.23)=-1.47
therefore, x=1.47/0.0381=38.5741 minutes ANSWER
waiting fewer than x minutes is 1-e^(-0.0381*x) and that is 0.47.
-e-(0.0381x)=-0.53
e^(-0.0381x)=0.53, this is waiting longer than x minutes
ln both sides and -0.0381x=-0.635
x=16.6667 minutes or 50/3 minutes ANSWER
check that 1-e^(-0.0381*16.6667)=1-e^(-0.6350)=1-0.5299=0.47.