Question

The Krasnapolski is a top-of-the-line hotel in Amsterdam, the Netherlands. Among their many services, they rent bicycles to guests. The bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. On average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. Guests keep bicycles for four days on average, with a standard deviation of two days. Remember: any time you see the term "random" associated with the job arrivals it means the coefficient of variation is equal to one; that is, the standard deviation in the time between arrivals is equal to the mean time between arrivals.

How long does a guest on average have to wait for a bike?

1. Approximately 47 minutes

2. Approximately 4 days

3. Approximately 24 hours

4. Approximately 0.033 hours

Answer 1

Sol:

Let X is random variable.

and X follows normal follows normal distribution with mean 4 days and variance 4 days.

we know that ,

~ N(

standard deviation of =/

Z score is

Z = ( - ) //

we want to find , p(10) = P(Z (10-4)/2/) = P(Z21.213) =1

So guest has to wait for approximately 1 day i.e 24 hours.