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Example 5.9 from Statistics, 5.3 The Exponential Distribution (Optional)
a. What is the probability that a computer part lasts more than seven years?
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.
a. Let x = the amount of time (in years) a computer part lasts.
Find P(x > 7). Draw the graph.
Since P(X < x) = 1 – e–mx then P(X > x) = 1 – (1 – e–mx) = e-mx
P(x > 7) = e(–0.1)(7) = 0.4966. The probability that a computer part lasts more than seven years is 0.4966.
How did it go?