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