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.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction