# Statistics

posted by
**Roshelle**
.

Let x and y be the amounts of time (in minutes) that a particular commuter must wait for a train on two independently selected days. Define a new random variable w by w = x + y, the sum of the two waiting times. The set of possible values for w is the interval from 0 to 2a (because both x and y can range from 0 to a). It can be shown that the density curve of w is as pictured (this curve is called a triangular distribution, for obvious reasons!)

Answer the following questions assuming a = 50, b = 0.02.

What is the probability that w is less than 50? Less than 25? Greater than 75?What is the probability that w is between 25 and 75?