Chapter 11.4, Problem 1MP

Use the probability density function given in Example 1 to find the probability that the individual waits:

(A)    Between 0 and 10 minutes

(B)    Between 10 and 20 minutes

(C)    Between 17 and 27 minutes

Waiting Time A bus arrives every 30 minutes at a particular bus stop. If an individual arrives at the bus stop at a random time (that is, with no knowledge of the bus schedule), then the random variable X, representing the time this individual must spend waiting for the next bus, is said to be uniformly distributed on the interval [0, 30]. The probability density function for this uniformly distributed random variable is

     $f\left(x\right)=\{\begin{array}{ll}\frac{1}{30}\hfill & \text{if}0\le x\le 30\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$