Using calculus, it can be shown that the area under the exponential distribution curve is P(X = x) =

Using calculus, it can be shown that the area under the
exponential distribution curve is

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P(X ≤ x) = 1 – e–kx.

a) What is the maximum value of P(X ≤ x)?

For what value of x does this maximum occur?

b) Use this equation for P(X ≤ x) to determine the
accuracy of the estimates for P(X ≤ 3) in Example 2.

c) Account for the difference between the estimates and the
value calculated using the equation above.

d) How could you improve the accuracy of the estimates?