Find the probability?

Answers for 3b and 3c are 0.8145 and 0.02

Answers for 4a and 4b are 0.657 and 0.2142

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  • 3 months ago
    Favourite answer

    Assuming a normal distribution we have:

    µ = 1000(0.1) = 100 and σ = √(1000 x 0.1 x 0.9) = √90

    b) We require P(90 ≤ x ≤ 115)...so, using a continuity correction we have:

    P(89.5 < x < 115.5)

    i.e. P[(89.5 - 100)/√90 < z < (115.5 - 100)/√90]

    so, P(-1.11 < z < 1.63)

    Hence, P(z < 1.63) - P(z < -1.11)

    i.e. P(z < 1.63) - P(z > 1.11)

    or, P(z < 1.63) - (1 - P(z < 1.11))

    => P(z < 1.63) + P(z < 1.11) - 1

    From normal tables we get:

    0.9484 + 0.8665 - 1 = 0.815

    c) We require P(x ≥ 120)...so, again using the continuity correction we have:

    P(x > 119.5) => P(z > (119.5 - 100)/√90)

    so, P(z > 2.06) => 1 - P(z < 2.06)...and from tables we get:

    1 - 0.9803 => 0.0197 = 0.02

    :)>

     

  • 3 months ago

    4a)

    p(at least 7 successful faxes) =

    p(7 successful faxes or 8 successful faxes) =

    p(7 successful faxes) + p(8 successful faxes) =

    0.85^7 * (1 - 0.85)^(8 - 7) * 8C7 + 0.85^8 * (1 - 0.85)^(8 - 8) * 8C8 =

    0.3206 * 0.15 * 8!/(7!(8 - 7)!) + 0.2725 * 1 * 8!/(8!(8 - 8)!) =

    0.3206 * 0.15 * 8 +0.2725 * 1 * 1 =

    0.657

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