$\"\"$

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(a)

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The exponential density function is $\"\"$ , where is $\"\"$ is some constant and $\"\"$ is in hours.

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Mean $\"\"$ .

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$\"\"$ .

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Thus, $\"\"$ .

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$\"\"$

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Find the probability that a customer has to wait more than $\"\"$ .

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$\"\"$

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Therefore, the probability that a customer has to wait more than $\"\"$ is $\"\"$ .

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$\"\"$

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(b)

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Find the probability that a customer is served within the first $\"\"$ .

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$\"\"$

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Therefore, the probability that a customer is served within the first $\"\"$ is $\"\"$ .

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$\"\"$

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(c)

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The manager wants to give hamburgers only to only $\"\"$ of her customers.

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Therefore, the probability that the customer gets a hamburger must be $\"\"$ .

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The probability that the customer has to wait for more than $\"\"$ is

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$\"\"$

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Find the value of $\"\"$ by equating the integral to $\"\"$ .

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$\"\"$

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$\"\"$

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Take natural logarithm on both sides.

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$\"\"$

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Anyone who waits for more than $\"\"$ gets a free hamburger.

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$\"\"$

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(a)

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The probability that a customer has to wait more than $\"\"$ is $\"\"$ .

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(b)

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The probability that a customer is served within the first $\"\"$ is $\"\"$ .

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(c)

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Anyone who waits for more than $\"\"$ gets a free hamburger.