### Let x denote the length in minutes of a long-distance

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Let X denote the length in minutes of a long-distance telephone conversation. Assume that the density for X is given by

f(x)=(1/10)e^(-x/10) where x>0

a. Verify that f is a density for a continuous random variable.

b. Assuming that f adequately describes the behavior of the random variable X, findthe probability that a randomly selected call will last at most 7 minutes; at least 7 minutes; exactly 7 minutes.

c. would it be unusual for a call to last betweel 1 and 2 minutes? Explain based on the probabliity of this occuring.

d. Sketch the graph of f and indicate in the sketch the area corresponding to each of the probabilities found in part b.

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