Question

Suppose each day an operator receives 100 independent calls and the length of each call is...

  1. Suppose each day an operator receives 100 independent calls and the length of each call is Exponentially distributed with mean 1.8min.

    (a) If the operator can only work for 200min, find the probability that the length of calls will exceed this work time.

    (b) If the mean (1.8min) of the calls was unknown what statistic would you use to estimate this mean? What is the probability that this estimator would result in an error that is greater than 2?

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Answer #1

The length of each call is Exponentially distributed with mean 1.8 min.

a) The total duration of calls is . According to Central Limit Theorem (CLT),

has approximate normal distribution with .

The probability that the length of calls will exceed this work time is

c) The mean of the calls is best estimated by using the statistic, sample mean . Thus,

"What is the probability that this estimator would result in an error that is greater than 2 ?"

is it 2 or 2% ? An error of 2 is highly unlikely.

If it is 2%,

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