Question 1131616
The probability function for an exponential distribution is given by:
{{{P(x) = lambda*e^(-lambda*x)}}}
An exponential distribution has a mean of {{{1/lambda}}}
Therefore, {{{lambda = 1/26.23 = 0.03812}}}
To find the probability of waiting less than X minutes, we have to integrate P(x) from 0 to x<=X
{{{int( lambda*e^(-lambda*x), dx ) = (-1/lambda)*(lambda*e^(-lambda*x)-1))}}}
Evaluating the integral from 0 to X and taking the log of both sides, we get:
{{{ln(0.53) = -lambda*X -> X = 16.6547}}}
Ans: 16.6547 mins