The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4.6 minutes. a. Calculate the ex

Question

The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4.6 minutes. a. Calculate the expected arrival time. (Round your answer to 2 decimal place.) b. What is the probability that an elevator arrives in less than 3.5 minutes? (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) c. What is the probability that the wait for an elevator is more than 3.5 minutes? (Round intermediate calculations to at least 4

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Skylar 2 hours 2021-10-14T13:47:58+00:00 1 Answer 0

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    2021-10-14T13:49:42+00:00

    Answer:

    a. 2.30 minutes

    b. 0.761

    c. 0.239

    Step-by-step explanation:

    Since this is a uniform distribution, the probability distribution function for any given time between 0 and 4.6 minutes is:

    P(X \leq x)=\frac{x-0}{4.6-0}=\frac{x}{4.6}

    a. The expected arrival time is the average waiting time, at an uniform distribution, the average is:

    E(X) = \frac{4.6+0}{2}=2.30\ minutes

    b. The probability for X ≤ 3.5 is:

    P(X \leq 3.5)=\frac{3.5}{4.6} \\P(X \leq 3.5)=0.761

    c. The probability for X ≥ 3.5 is:

    P(X \geq 3.5)=1-P(X \leq 3.5)=1-0.761\\P(X \geq 3.5)=0.239

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45:7+7-4:2-5:5*4+35:2 =? ( )