Answer:
(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 <em>X</em> = the waiting time for the bus at the parking lot.
The random variable <em>X</em> is uniformly distributed with parameters <em>a</em> = 0 to <em>b</em> = 15.
The probability density function of <em>X</em> 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 <em>X</em> 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.