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statistics homework problem ?

suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. 

A) what proportion of light bulbs will last more than 61 hours?

B) what proportion of light bulbs will last 52 hours or less?

C) what proportion of light bulbs will last between 59 and 62 hours?

D) what is the probability that a randomly selected light bulb lasts less than 46 hours?

1 Answer

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  • 2 months ago

    A) P(x > 61) => P(z > (61 - 57)/3.5)

    so, P(z > 1.143) = 1 - P(z < 1.143)

    From normal tables we have:

    1 - 0.8735 = 0.1265

    i.e. 12.7%

    B) P(x < 52) => P(z < (52 - 57)/3.5)

    so, P(z < -1.429) => 1 - P(z < 1.429)

    From tables we get:

    1 - 0.9235 = 0.0765

    i.e. 7.7%

    C) P(59 < x < 62) => P[(59 - 57)/3.5 < z < (62 - 57)/3.5]

    so, P(0.571 < z < 1.429)

    => P(z < 1.429) - P(z < 0.571)

    From tables we get:

    0.9235 - 0.7160 = 0.2075

    i.e. 20.8%

    D) P(x < 46) => P(z < (46 - 57)/3.5)

    so, P(z < -3.143) => 1 - P(z < 3.143)

    From tables we get:

    1 - 0.99916 = 0.00084

    i.e. 0.084%

    :)>

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