The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. A. Wh

Question

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. A. What is the probability that a flight is more than 140 minutes?B. What is the distribution’s mean? C. What is the distribution’s standard deviation? D. What is the probability that a flight is less than 135 minutes?

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Madelyn 2 weeks 2021-09-10T13:20:37+00:00 1 Answer 0

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    2021-09-10T13:21:43+00:00

    Answer:

    a) 33.33%)

    b) 135 minutes

    c) 8.66 min

    d) 50%

    Step-by-step explanation:

    a) the probability for a uniform distribution is

    P(b<X<a) = (a-b)/(c-d) , where c and d are the maximum and minimum values

    therefore the probability that the flight is more than 140 minutes ( and less than 150 since it is the maximum value)

    P(140<X<150) = (a-b)/(c-d) = (150-140)/(150-120) = 10/30 = 1/3 (33.33%)

    b) the mean (expected value) for a uniform probability distribution is

    E(X) = (c+d)/2 = (120+150)/2 = 135 minutes

    c)  the standard deviation for a uniform probability distribution is

    σ²(X)= (c-d)²/12 = (150-120)²/12 = 75 min²

    σ = √75 min² = 8.66 min

    b) following the same procedure as in a)

    P(120<X<135) = (a-b)/(c-d) = (135-120)/(150-120) = 15/30 = 1/2 (50%)

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