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Example 5.8 from Statistics, 5.3 The Exponential Distribution (Optional)
(part 1)
a. Using the information in Example 5.7, find the probability that a clerk spends four to five minutes with a randomly selected customer.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
a. Find P(4 < x < 5). The cumulative distribution function (CDF) gives the area to the left.
Figure 5.23NOTE
You can do these calculations easily on a calculator.
The probability that a postal clerk spends four to five minutes with a randomly selected customer is P(4 < x < 5) = P(x < 5) – P(x < 4) = 0.7135 − 0.6321 = 0.0814.Using the TI-83, 83+, 84, 84+ Calculator
On the home screen, enter (1 – e^(–0.25*5))–(1–e^(–0.25*4)) or enter e^(–0.25*4) – e^(–0.25*5).
How did it go?