The time (in minutes) between telephone calls at an insurance claims office has the following exponential probability distribution. $$f(x)=.50 e^{-50 x} \quad \text { for } x \geq 0$$ a. What is the mean time between telephone calls? b. What is the probability of having 30 seconds or less between telephone calls? c. What is the probability of having 1 minute or less between telephone calls? d. What is the probability of having 5 or more minutes without a telephone call?
Added by Domingo S.
Step 1
The expected value (mean) of an exponential distribution with parameter λ is given by: $$E(x) = \frac{1}{\lambda}$$ In this case, the parameter λ is 50. So, the mean time between telephone calls is: $$E(x) = \frac{1}{50}$$ $$\boxed{E(x) = 0.02}$$ b. Show more…
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Calls to Insurance Claims Office. The time (in minutes) between telephone calls at an insurance claims office has the following exponential probability distribution. $$ f(x)=.50 e^{-50 x} \quad \text { for } x \geq 0 $$ What is the mean time between telephone calls? b. What is the probability of having 30 seconds or less between telephone calls? c. What is the probability of having 1 minute or less between telephone calls? What is the probability of having 5 or more minutes without a telephone call?
The time (in minutes) between telephone calls at an insurance claims office has the exponential probability distribution: f(x) = 0.40e^{-0.40x} for x ≥ 0 a. What is the mean time between telephone calls? Mean time (μ) = 2.5 minutes b. What is the probability of 45 seconds or less between telephone calls? (Note: 45 seconds = 0.75 minutes) If required, round your answer to four decimal places. P(x ≤ 0.75) = 0.2592 c. What is the probability of 3 minute or less between telephone calls? If required, round your answer to four decimal places. P(x ≤ 3) = 0.6988 d. What is the probability of 7 or more minutes without a telephone call? If required, round your answer to four decimal places. P(x ≥ 7) = 0.091
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