The activity completion time of each of the 5 critical activities of a project follows normal distribution. If the mean activity completion

Question

The activity completion time of each of the 5 critical activities of a project follows normal distribution. If the mean activity completion time of each activity is 2 weeks, and the standard deviation of the activity completion time of each of the critical activity is 10, then what is the probability that the project would take between 9 and 13 week?

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Sadie 3 weeks 2021-12-30T21:45:09+00:00 1 Answer 0 views 0

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    2021-12-30T21:46:33+00:00

    Answer:

    P(x = 9) and P(x = 13) is:

    0.6551965

    Step-by-step explanation:

    By Z score,

    Z = \frac{x - 2}{\frac{\sigma}{\sqrt{n}}},

    P(x = 9 ) = P(Z = \frac{9 -2 }{\frac{10}{\sqrt{5}}} )

    P(x =13) = P(Z = \frac{13 -2 }{\frac{10}{\sqrt{5}}} )

    And these give:

    P(x = 9) ==>  P(Z = 0.7) = 0.7580363

    P(x = 13) ==>  P(Z = 1.1) = 0.8643339

    Therefore, the probability that the project would take between 9 and 13 week = P(x = 9) * P(x =13) =  0.6551965.

    For replication, see the R codes below:

    Z1 = (9 – 2)/(10/sqrt(length(5)))

    a = pnorm(Z1)

    Z2 = (13 – 2)/(10/sqrt(length(5)))

    b = pnorm(Z2)

    a*b

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