The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that λ = (a) What is the probability that a call to the helpline lasts less than 10 minutes? (b) What is the probability that a call to the helpline lasts more than 30 minutes? (c) What is the probability that a call lasts between 20 and 30 minutes? = 0.05. (Round your answer to four decimal places.

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The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that \(\lambda = \frac{1}{20} = 0.05\). (Round your answer to four decimal places.)

(a) What is the probability that a call to the helpline lasts less than 10 minutes?

\[ \_\_\_\_\_\_ \]

(b) What is the probability that a call to the helpline lasts more than 30 minutes?

\[ \_\_\_\_\_\_ \]

(c) What is the probability that a call lasts between 20 and 30 minutes?

\[ \_\_\_\_\_\_ \]

(d) Tchebysheff's Theorem says that the interval \(20 \pm 2(20)\) should contain at least 75% of the population. What is the actual probability that the call times lie in this interval?

\[ \_\_\_\_\_\_ \]
Transcribed Image Text:The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that \(\lambda = \frac{1}{20} = 0.05\). (Round your answer to four decimal places.) (a) What is the probability that a call to the helpline lasts less than 10 minutes? \[ \_\_\_\_\_\_ \] (b) What is the probability that a call to the helpline lasts more than 30 minutes? \[ \_\_\_\_\_\_ \] (c) What is the probability that a call lasts between 20 and 30 minutes? \[ \_\_\_\_\_\_ \] (d) Tchebysheff's Theorem says that the interval \(20 \pm 2(20)\) should contain at least 75% of the population. What is the actual probability that the call times lie in this interval? \[ \_\_\_\_\_\_ \]
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