Answer:
The probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.
Step-by-step explanation:
The random variable <em>T</em> is defined as the amount of time a customer spends in a bank.
The random variable <em>T</em> is exponentially distributed.
The probability density function of a an exponential random variable is:
The average time a customer spends in a bank is <em>β</em> = 10 minutes.
Then the parameter of the distribution is:
An exponential distribution has a memory-less property, i.e the future probabilities are not affected by any past data.
That is, <em>P</em> (<em>X</em> > <em>s</em> + <em>x</em> | <em>X</em> ><em> s</em>) = <em>P</em> (<em>X</em> > <em>x</em>)
So the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is:
P (X > 15 | X > 10) = P (X > 5)
Thus, the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.