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2 November, 06:08

The time (in minutes) until the next bus departs a major bus depot follows a uniform distribution from 25 to 46 minutes. Let X denote the time until the next bus departs. The distribution is and is. The mean of the distribution is μ=. The standard deviation of the distribution is σ=. The probability that the time until the next bus departs is between 30 and 40 minutes is P (30

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  1. 2 November, 06:48
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    The distribution is uniform and is continuous probability distribution.

    The mean of the distribution is μ = 35.5 minutes.

    The standard deviation of the distribution is σ = 6.06

    P (30
    Step-by-step explanation:

    a. The amount of time in minutes until the next bus departs is uniformly distributed between 25 and 46 inclusive.

    The distribution is uniform and is continuous probability distribution.

    b. Let X be the number of minutes the next bus arrives and a = 25, b = 46. Hence mean = a+b/2 = 25 + 46 / 2 = 35.5 minutes.

    The mean of the distribution is μ = 35.5 minutes.

    c. Standard deviation = √ (b-a) ²/12

    Standard deviation = √ (46-25) ²/12 = √ (21) ²/12 = √441/12=√36.75 = 6.06

    The standard deviation of the distribution is σ = 6.06

    d. P (30
    For this we draw a graph. It is also called the rectangular distribution because its total probability is confined to a rectangular region with base equal to (b-a) and height 1 / (b-a).

    This can be calculated as

    P (30
    = (40-30) * (1 / 21) = 10/21 = 0.476
  2. 2 November, 07:41
    0
    Step-by-step explanation:

    The distribution is Uniform and is continuous.

    We are given a = 25 and b = 446

    The mean of the distribution is

    Mean = µ = (a + b) / 2

    = (25 + 44) / 2

    = 34.5

    The standard deviation of the distribution is

    SD = σ = (b - a) / sqrt (12)

    = (46 - 25) / sqrt (12)

    = 21/3.464102

    = 6.062minutes

    SD = σ = 6.062minutes

    Now, we have to find P (30
    P (30
    = (40 - 30) / (46 - 25)

    = 10/19

    = 0.4762

    Required probability = 0.4762

    Now, we have to find the value of a for which P (X≤a) = 0.9

    We have, P (X≤a)

    = (a - 25) / (46 - 25)

    = (a - 25) / 21

    (a - 25) / 21 = 0.9

    (a - 25) = 0.9*21

    So, a = 18.9 + 25 = 43.

    a = 43.9

    = 43.9minutes
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