Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours. The probability that a li

Question

Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours. The probability that a light bulb picked at random will last between 1400 and 1500 hours is about:

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bonexptip 3 years 2021-07-20T15:02:58+00:00 1 Answers 52 views 0

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  1. thuhuong
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    2021-07-20T15:03:58+00:00
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    Answer:

    The probability that a light bulb picked at random will last between 1400 and 1500

    P(14 00≤X≤1500) = 0.032

    Step-by-step explanation:

    Explanation:-

    Given that mean of the Population = 1000

    Given that the standard deviation of the Population = 250 hours

    Let ‘X’ be the random variable in a normal distribution

    Let  X = 1400

    Z = \frac{X-mean}{S.D} = \frac{1400-1000}{250} = 1.6

    Let X = 1500

    Z = \frac{X-mean}{S.D} = \frac{1500-1000}{250} = 2

    The probability that a light bulb picked at random will last between 1400 and 1500

    P(x₁≤ X ≤x₂) = P(Z₁≤ Z ≤z₂)

                       = A( Z₂ ) -A(Z₁)

    P(1400≤X≤1500)  = P(1.6≤ Z ≤2)

                                =  A(2 ) -A(1.6)

                               =  0.4772-0.4452

                              = 0.032

    Final answer:–

    The probability that a light bulb picked at random will last between 1400 and 1500

    P(14 00≤X≤1500) = 0.032

                       

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