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In a benchmark study, a fast food restaurant had an average service time of 2.4 minutes. Assume that the service time for the fast food restaurant has an exponential distribution. (Round your answers to four decimal places.) (a) What is the probability that a service time is less than or equal to one minute

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MrRoyal

Answer:

[tex]P(x \le 1)= 0.9093[/tex]

Step-by-step explanation:

Given

[tex]\lambda = 2.4[/tex] -- mean

Required

Determine [tex]P(x \le 1)[/tex]

This is calculated using:

[tex]P(X \le x)= 1 - e^{-\lambda x}[/tex]

So:

[tex]P(x \le 1)= 1 - e^{-2.4 * 1}[/tex]

[tex]P(x \le 1)= 1 - e^{-2.4}[/tex]

[tex]P(x \le 1)= 1 - 0.0907[/tex]

[tex]P(x \le 1)= 0.9093[/tex]

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