The shuttle bus from your parking lot and your office building operates on a 15 minute schedule. You arrive at the parking lot at a random time during the bus’s cycle, that is, the time you have to wait for the bus is uniformly distributed over the interval from 0 to 15. What is the standard deviation of your waiting time? What is the probability that you will have to wait more than 2 standard deviations?

(a) The standard deviation of your waiting time is 4.33 minutes.

(b) The probability that you will have to wait more than 2 standard deviations is 0.4227.

Step-by-step explanation:

Let X = the waiting time for the bus at the parking lot.

The random variable X is uniformly distributed with parameters a = 0 to b = 15.

The probability density function of X is given as follows:

(a)

The standard deviation of a Uniformly distributed random variable is given by:

Compute the standard deviation of the random variable X as follows:

Thus, the standard deviation of your waiting time is 4.33 minutes.

(b)

The value representing 2 standard deviations is:

Compute the value of P (X > 8.66) as follows:

Thus, the probability that you will have to wait more than 2 standard deviations is 0.4227.