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A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes (i.e. the mean number of calls answered in a minute is ). What proportion of callers is put on hold longer than 2.8 minutes?

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Karabo99

Answer:

The proportion of callers is put on hold longer than 2.8 minutes is 0.3679

Explanation:

μ = 2.8 , λ = 1/2.8 ,

By the exponential distribution:

P(x>k) = exp(-λk)

          = exp(-2.8/2.8)

          = 0.3679

Therefore, The proportion of callers is put on hold longer than 2.8 minutes is 0.3679

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